Maybe we were just lucky, cause if Vons had called my CC company, they would have found out that my billing address was not, in fact, that of the Camelot hotel where we were staying. Basically pretend your blling address is the hotel address. We tried it, realizing that there was a possiblility of getting "caught" and not having our groceries delivered, so we had a backup plan that we didn't end up needing to use.
Give it a try, and good luck!