Spoiler Alert: This piece may contain spoilers from any material of A Song of Ice and Fire.
If you read A Song of Ice and Fire as if it is a mystery series, you quickly catch on to the fact that George R. R. Martin likes to use songs and other tales to give you clues about secrets within the greater story. These tales are more than mere flavor; they have double meanings and hidden messages. Sometimes the characters presenting them are unaware of the implications, but George is using them to give clues to the reader.
Several of these items are pertinent to the Mance Rhaegar Theory, such as the tale of Bael the Bard, the song The Dornishman's Wife, and Mance Rayder's own account of his shadowcat attack. Others have discussed these, though I plan to do the same eventually. In this post, however, I would like to address a connection that I have not yet seen made.
"Old Nan told him a story about a bad little boy who climbed too high and was struck down by lightning, and how afterward the crows came to peck out his eyes. Bran was not impressed. There were crows' nests atop the broken tower, where no one ever went but him, and sometimes he filled his pockets with corn before he climbed up there and the crows ate it right out of his hand. None of them had ever shown the slightest bit of interest in pecking out his eyes."
Nan's tale seems to be a reference to - you guessed it - Rhaegar Targaryen. Consider that those in Winterfell might view him as "a bad little boy who climbed too high" because, as the Official Story goes, he abused his power as the prince to abduct Lyanna Stark, the daughter of a great lord who was already engaged to another great lord. That latter lord - the Storm Lord - is the lightning that struck him down.
The part about the eyes isn't quite as clear, but I suspect it means that the Night's Watch erased his identity. Crows are a common reference to the Watch, and Rhaegar's eyes were his most defining characteristic. Old Nan may or may not be aware of Rhaegar's hiding, but George can still use her tale to send a hidden message to the reader.
Jaime also recalls that crows "had feasted on Rhaegar Targaryen after the Trident." Crows often start with the eyes.
What's cute is that Bran isn't buying the Official Story. This is George's way of saying that you shouldn't either. Bran's own take has significance, too. Bran is being used by George to further relay the hidden meaning to the reader.
"where no one ever went but him," describes the isolation that would protect Rhaegar, especially at the Shadow Tower. Rhaegar's motivation for getting involved in northern affairs may have also been fueled by the fact that few go there anymore and the Watch is dwindling. It needs a man with his special gift for uniting people in order to weather the coming storm.
"sometimes he filled his pockets with corn before he climbed up there and the crows ate it right out of his hand." This may mean that he disguised himself and they bought it - hook, line, and sinker.
"None of them had ever shown the slightest bit of interest in pecking out his eyes." Nobody wants Rhaegar's new throne. He is far removed from the feuding now.
As always, I welcome any corrections or additions to help strengthen the theory.