So...here's the full crackpot theory. It makes sense to me and explains multiple characters:
Ashara has given birth to what is essentially a Blackfyre, the bastard son of Aerys. Ned has the trueborn heir in Lyanna's son Aegon (if, as I believe, Rhaegar and Lyanna had secretly wed). Varys, being Varys, is aware of the goings on and comes to them at Starfall and concocts his master scheme. Targs are dropping like flies and the two children need protecting.
The first two stories that Varys puts out are that Ashara, not Lyanna, leapt to her death from a tower and that she and Ned were lovers. This allows for Ashara to disappear with her child, and gives Ned a story for where Aegon (Jon)came from. Varys enlists the help of Jon Connington, Rhaegar's best friend and Aery's HOTK. He tells Jon that the child that Ashara has is Rhaegar's son Aegon and that he must flee Westeros and keep him safe. Not sure, but Varys may not actually know which child is which himself and may believe that it is
Aegon that he's sending with Connington. Posing as Septa Lemore, Ashara goes with him to help protect her son. Varys puts out the third story about Connington fleeing Westeros in shame and Grief over his defeat and Rhaegar's death, which is partly true.
That leaves Ned in Westeros with the true Aegon and a decent cover story. Aegon remains at Starfall and is wet nursed by Wylla until Ned is ready to return to Winterfell. Ned comes up with the name "Jon Snow", possibly "Jon" from the involvement with Connington.
I have a ton of other references that actually support this theory, including the irony of Jon Snow's decision to swap Mance's child with Gilly's to protect the true "prince".
This post was edited on 7/6 at 3:04 pm