Signing up for AirBnB exposes you to the same risks as if you sublet your living space the same way it would in a traditional transaction. Rent to shitty people? You're responsible. AirBnB does not guarantee a pleasant experience, nor is it required to make this person whole by getting them removed from whatever tenant blacklist they're on.

Welcome to bumps on the "sharing economy" road.

Edit: it appears property management companies are using public court records to screen this person, preventing them from renting. That's not an AirBnB problem, that's a fair housing legislation problem.