It makes pretty clear sense to me. She got panicked when Raffaele changed his story and she no longer had a clear alibi. She was counting on Raffaele, they were counting on each other to be each other's alibi. So when that showed signs of unraveling, she panicked.
I don't know what the confusion is, really. She was a guilty person who panicked. MOO.
In all honesty, if I was guilty of the murder, in the same situation with my alibi gone, I would do and say whatever necessary to even temporarily buy myself some time.
Maybe she didn't think. Maybe she thought, but figured by the time police figure it out, she'll be back safe in America with her Mom....she probably thought, "how can they get me there?" That would make perfect sense to me. Run away. Go back to your country, go back to safety, how could they "catch" her there?
At the time, I don't think she would be thinking of extradition, blah blah. Maybe she thought she'd get "caught," but how would they physically bring her back to Italy to put her in jail?
The thing I would be thinking at the time was, "get me back to the U.S." Anything to get me back to the U.S..