This is the most believable theories out there. And the wrter also said that the fans have already guessed right.
Likely true. A bit on Rhaegar from book references: He was a singer and a voracious reader as a youth until he read a prophecy that changed him. The prophecy was about "the prince that was promised" and at first Rhaegar believed he was it, approaching the Targaryen master at arms for training, saying "it seems I am to be a warrior".
And then from Dany's vision at the House of the Undying, it seems Rhaegar changed his mind about who the prince is: A scene with Rhaegar, Elia, and their newborn son Aegon. Elia asked him to compose a song for Aegon and Rhaegar says something like "he has one already, his is the song of ice and fire".
From the above, we can infer that Rhaegar now believed that the "prince that was promised" is his son Aegon and that based on his understanding of the prophesy, the product of a union between ice and fire. Now I don't quite get how a Martell and Targaryen union could represent ice and fire but it seems that later on Rhaegar realized that ice and fire was rightly represented by Stark and Targaryen. This may have influenced him to woo Lyanna at the Harrenhal tilt where famously, he broke tradition and gave the winner's flowers to Lyanna instead of Elia.
Remember Peter Baelish question to Sansa in the Winterfell crypt? "How many tens of thousands had to die because Rhaegar chose your aunt?.