I can see how someone who had already been in trouble with the law would make something up showing that they were completely out of the area when it happened - even if they truly had nothing to do with it - because they might think it will appease the cops and they'll be left alone. Not a smart thing to do, but some of them might have thought they would be able to pull one over on the cops.
Someone who has already been in trouble with the law knows that lying to LE never works. LE doesn't take you word for it, they check up on your story.