Thanks for clearing that up, Paraguy, I couldn't remember Reagar's name. This is the predominant theory on the Internet. That Lyanna and Reagar were secret lovers, and she did not want to marry Robert. She hidout and had the baby that tower in Dorne, but died as Ned arrived to "rescue" her. He claimed her boy as his own so he would escape certain death by the Targareyens. That still makes Jon Snow 1/2 Stark... And, royal bloodlines on both sides. Sure doesn't look like he's got a drop of blonde DNA in him, to me, though.
I don't know how the story goes in the books.
A/B