This theory posits two things:
For the first point, let's take a look at a couple very telling quotes from Daenerys X, AGOT, only a few paragraphs apart:
As she climbed down off the pyre, she noticed Mirri Maz Duur watching her. “You are mad,” the godswife said hoarsely.
The key word here is "hoarsely." First off, I tend to pay extra attention to adverbs that follow words like "said." Writers tend to use them sparingly, because it can make prose seem overwrought to use them all the time. But this is beside the point; "hoarsely" is important here either way. Mirri's voice is not harsh because of her night of screaming and singing to keep Drogo alive. She has spoken normally since then, and it was long enough ago that if she lost her voice it would have returned. She speaks hoarsely because she sees Dany put the dragon eggs on the pyre. She speaks hoarsely because she is afraid, because she knows what this means.
“...I remember what you told me. Only death can pay for life.” Mirri Maz Duur opened her mouth, but made no reply. As she stepped away, Dany saw that the contempt was gone from the maegi’s flat black eyes; in its place was something that might have been fear. Then there was nothing to be done but watch the sun and look for the first star.
Now we have somewhat of a confirmation both for Mirri and the reader. She has bound Mirri to the pyre and explicitly told Mirri that this is a death-for-life transaction. But she obviously isn't bringing Drogo back; he is dead and on the pyre, and there is a horse slaughtered in the pyre with him, to ride in the afterlife. Dany has no intention of buying Drogo's life again. What Mirri fears is exactly what Daenerys intends to buy: life for the three dragons. This in and of itself is no surprise. It is common knowledge amongst fervent readers of A Song of Ice and Fire, a knowledge well-rooted in the text, that Dany was very much intentionally trying to wake her dragons from those stone eggs. But I've never seen it suggested that Mirri fears the dragons, only a general acceptance that she fears dying. I do not think that is true, as seen in Daenerys IX:
“Saved me?” The Lhazareen woman spat. “Three riders had taken me, not as a man takes a woman but from behind, as a dog takes a bitch. The fourth was in me when you rode past. How then did you save me? I saw my god’s house burn, where I had healed good men beyond counting. My home they burned as well, and in the street I saw piles of heads. I saw the head of a baker who made my bread. I saw the head of a boy I had saved from deadeye fever, only three moons past. I heard children crying as the riders drove them off with their whips. Tell me again what you saved.”
Mirri Maz Duur laughed cruelly. “Look to your khal and see what life is worth, when all the rest is gone.”
Mirri Maz Duur does not fear death. Everything she has is gone. She welcomes death, but not on that pyre. On the pyre she talks big, but her eyes and hoarse voice betray fear. Why, if she does not fear death? Because she fears what the death buys. But why fear dragons specifically? She will not be around to be hurt by them, and it is Daenerys's choice to use her life for them. Isn't it? But I argue that Mirri isn't just fearing the dragons, but also regretting that she is directly responsible for them. Right before the above passage she says:
“The stallion who mounts the world will burn no cities now. His khalasar shall trample no nations into dust.”
Is that so? It is true, Rhaego cannot burn any cities; he is dead. But here Mirri is so confident that she has saved the world from destruction wrought by Daenerys's children. Then, on the pyre, she realizes that by killing Rhaego, she has personally brought about the events that would give birth to something that would burn cities and trample nations. If she had simply lied to Daenerys and said there was nothing she could do, let Drogo die and Rhaego live, then a new khal would have slaughtered Rhaego (or, as I suggest elsewhere, Rhaego would have been a stillborn anyways) and Dany would have been taken to the dosh khaleen. But instead she kills Rhaego to be safe, thinking Daenerys a simple, naïve girl who wants her husband back. It is her child Mirri need fear. This lapse in judgment causes her to teach Daenerys the most dangerous lesson she could have taught: "Only death can pay for life." Mirri realizes, as soon as Dany puts the eggs on the pyre and ties her to it, that she herself taught Daenerys how to do it, and now her life will pay to wake these dragons. She didn't save the world from burning, she herself condemned it.
So there you have that. Mirri doesn't fear death. She fears that, in her attempt to save the world from burning, she has instead guaranteed that it would burn. I intend to take this one step further, and show that Rhaego never was the stallion who mounts the world. It was always the dragons.
To show this, let's go back to the dosh khaleen where we first see Rhaego prophesied as the stallion who mounts the world:
Finally the crone opened her eye and lifted her arms. “I have seen his face, and heard the thunder of his hooves,” she proclaimed in a thin, wavery voice.
“The thunder of his hooves!” the others chorused.
“As swift as the wind he rides, and behind him his khalasar covers the earth, men without number, with arakhs shining in their hands like blades of razor grass. Fierce as a storm this prince will be. His enemies will tremble before him, and their wives will weep tears of blood and rend their flesh in grief. The bells in his hair will sing his coming, and the milk men in the stone tents will fear his name.” The old woman trembled and looked at Dany almost as if she were afraid. “The prince is riding, and he shall be the stallion who mounts the world.”
“The stallion who mounts the world!” the onlookers cried in echo, until the night rang to the sound of their voices.
I would like to add to this a quote from Daenerys IV, ADWD:
He shall be the stallion that mounts the world. Dany knew how it went with prophecies. They were made of words, and words were wind.
What I want to ask is... is that so? I can't personally think of a single "prophecy" in this book series that has truly just flat-out not come to pass, and we have a quote from GRRM himself that suggests all prophecies will come true in some way:
Prophecies are, you know, a double edge sword. You have to handle them very carefully; I mean, they can add depth and interest to a book, but you don’t want to be too literal or too easy... In the Wars of the Roses, that you mentioned, there was one Lord who had been prophesied he would die beneath the walls of a certain castle and he was superstitious at that sort of walls, so he never came anyway near that castle. He stayed thousands of leagues away from that particular castle because of the prophecy. However, he was killed in the first battle of St. Paul de Vence and when they found him dead he was outside of an inn whose sign was the picture of that castle! So you know? That’s the way prophecies come true in unexpected ways. The more you try to avoid them, the more you are making them true, and I make a little fun with that.
The entire quote is important, but the above is especially relevant to what I've said with Mirri Maz Duur. She tried to prevent the "stallion who mounts the world" prophecy from coming true, but that's exactly how (I believe) it did come true.
The stallion prophecy isn't ever really regarded as anything other than a prophecy, and prophecies tend to come true. So why is it the only example we have of a prophecy not coming true? And why is it so much more unambiguous than any other prophecy we've had? It isn't very often that we get a prophecy that straight up says "X does Y." We get a glimpse into prophecy with Melisandre in ADWD, who herself admits how ambiguous it can be. It involves seeing things that aren't completely clear, especially to the prophesier. When Melisandre sees Bloodraven in the flames, we know what she's seeing because we as readers already know about him through Bran. Melisandre doesn't know exactly who it is. Then why does the crone at the dosh khaleen seem so confident that what she sees is Rhaego? Is it really that clear to her? I personally think it's a case of deduction on the crone's part: she sees the stallion, and assumes it to be Rhaego, because who else would it be? I argue that she sees a dragon, and assumes it to be Rhaego because Daenerys is "blood of the dragon." Why should it be a literal dragon, when they are all dead? What reason does the crone have to believe that a dragon should be literal? The thunder of hooves, or the thunderous flapping of massive wings? Riding as swift as the wind, or riding on the wind? Men in stone tents will tremble? Well, look at Harrenhal...
There is also an interesting bit of textual evidence (though by no means strong textual evidence from when Daenerys encounters Khal Jhoqo's khalasar, suggesting that Drogon may indeed be the stallion. From Daenerys X, ADWD:
A vast herd of horses appeared below them. There were riders too, a score or more, but they turned and fled at the first sight of the dragon. The horses broke and ran when the shadow fell upon them, racing through the grass until their sides were white with foam, tearing the ground with their hooves... but as swift as they were, they could not fly.
Again I ask: riding as "swift" as the wind (note the similar word choice), or riding on the wind?
But then, you ask, what if the crone saw a human face in her flames? I argue that that is not possible: I do not think that Rhaego's scaled appearance was due to Mirri Maz Duur. Of course, that is a matter for another theory.
Were Rhaego to be deformed and stillborn without bloodmagic, it sort of explains why Drogo was brought back to such a half-life. Mirri implies that he would have been this way anyways, but with such a monstrous baby that would have been dead as soon as it left the womb either way, what sort of life would that buy? Dany was lucky to buy a vegetable with that life. Though it may have been easy to blame Mirri for her kid's monstrous appearance, I don't think she was responsible. The evidence otherwise is simply too strong.
And if it's not Mirri that did it, and Rhaego would die anyway, that only solidifies that the "stallion" prophecy was either bullshit, or never about Rhaego at all. It was about her dragons, or at least Drogo, and Mirri realized in her last moments that in her attempt to prevent that doom, she instead brought it to fruition.