KnightBrolaire
SSO's unofficial pickup tester
I was just about to cite that part too. I find it highly improbable that littlefinger would have had a relationship with lyanna and she kept it a secret from ned. Plus, if Jon was related to littlefinger there would likely be some similarity in appearance, and they wouldn't have wasted so much time teasing us about lyanna/rhaegar. That would be one of the most unexpected but also asinine twists in a show since Andrea got killed off in Walking Dead.To your 3rd point:
While it doesn't prove Rhaegar secretly married Lyanna, it hints this is most likely what happened since at the Tourney at Harrenhal, Rhaegar gave the victor's wreath (crown of winter roses) to Lyanna Stark. Lyanna is said to love winter roses -- some fans believe Rhaegar even made it ahead of time specifically for her (knowing he had a good chance of winning the tournament).
To quote Ned Stark's dream:
And according to tradition in the Seven Kingdoms, when a winner dedicates his victory to a woman by giving her the crown of roses, it is usually a woman he loves and/or intends to court. This would explain why "all the smiles died" since it is scandalous to do this when 1) the woman is already married or 2) you are already married.
That would also explain why the marriage was in secret because it was "frowned upon".
Again, I'm not saying this is absolute fact but I think it's difficult to say otherwise.