It is possible to use PayPal instead of a credit card. When they made their Airbnb account, did they link their PayPal account or a credit card at that time? I'm pretty sure they had to pay for at least part of the reservation up front; when they got the reservation confirmation what form of payment was listed?
On a separate note, I had a guest contact me with all sorts of payment problems, which I ultimately contacted Airbnb to figure out. I thought I was doing him a favor. Turns out, he was trying to trick me into issuing him a 50% refund on his stay and left me a less-than-stellar review when it didn't work. I advise politely informing the guest that you have nothing to do with collecting payments and referring them to Airbnb customer service.
