Ugh! So sorry that happened to you, Lindsey. I've written in all over the forum lately, never trust that Airbnb has done any sort of background check on your guest(s). If you'd like me to run the name for you to see if he comes up with an existing record, I'd be more than happy to, just message me.
That said, and I'm not blaming you for their crime, but NEVER leave cash or credit card information laying about where guests can even think about accessing it. Even great guests will be looking in drawers, closets, etc. and it's definitely unwise for you to treat short term guests like you would longer term roommates who you have vetted yourself and invited personally to live with you.
Be careful out there. Let us know how Airbnb follows up with your case.