I don’t think it’s possible to call up a hotel and pay them to upgrade someone else’s room that you didn’t pay for to begin with.
It would certainly surprise me if you could, since you’d be committing someone else’s credit card. I’m sure Bialek called the Hilton before she came forward to make sure that her story couldn’t be “verified” by the Hilton.
It is possible because I’ve taken care of things like this for clients under special circumstance. However, you have to provide credit documentation and complete specific forms to do it. If Cain did this himself, he would have had to have provided copies of a credit card, ID, and a signature authorization to make it happen. If the records still exist, it could be easily verified.
I don’t believe someone in his position would ever do something like that or even know how to do it.