This is my theory on her claim: She knows it isn't Justin's baby but perhaps she thought he'd take pity on her and give her money to help her out with the baby anyways. She likely didn't think of the possibility that she could get sued for making the claim and that is the unfortunate thing about a lot of people these days...they don't think things through because surly if they did they wouldn't do such stupid things.
She probably didn't imagine that people would be looking at her life with a magnifying glass and a fine-toothed comb as well. I'm not a Justin fan, in fact I think my ears bleed everytime I hear "Baby, baby, baby... ooohh" but just because a crazy fan makes a claim doesn't mean it is anywhere near the truth. People will do anything for 15 minutes of fame, even if they have to use their baby to do it.
Then again, I'm not perfect and I shouldn't judge her but I guess it is too late for that.