It depends on the state, but if she is 20, the car and insurance and credit card are all in her name without anything affliated with her parents, then yes it's illegil.
However, if she is refuseing to follow the rules of the house, no matter what YOU think of them, then they have every right to boot her out. It's THEIR house, and THEIR rules. It's not like they threw a child out on the street.
If she has the ability to pay for a car, credit card payments, insurance etc.. let her get her own place to live. Her parents have every right to take away any privledge that they pay for. I don't have a lot of sympathy for the "they kicked her out", since no one I know at 20 doesn't have someone they can go bum a couch off of. Obviously she has, since she is staying with you.
She should be able to call the credit card company and let them know it was not her, and they will re-instate her card, with a security feature to make sure no one can cancel it that isn't her. (security question). If she has the spare key to the car, and removes it, then she's clear there. If the parents report it stolen, then she can easily tell the police, "Here's the title in my name, the insurance in my name, and the registration in my name. They filed a false report". If the parents don't call it in stolen, then all they did was take the key, which is petty, but not enough to bother with authorites. Since the parents did not USE the credit card, it's not identity theft, per se. It's again.. petty.
If any of it is in their names... at all, co-signing, using their insurance, etc.. they were within their rights.
Good luck with your friend. She should get her own place, and stop trying to live with mom and dad, if she wants to have her own rules.