Sounds like credit card fraud to me. The actual credit card transaction was correct.

It seems as though the problem is at Hilton (corporate/chain), not the hotel. Why punish the hotel for a problem they (probably) didn't create? Pick up the phone and call Hilton. Talking to someone directly means they can't misread or ignore your email.

Full Disclosure: One of my former hotel jobs involved responding to credit card chargebacks. It's a time-consuming process. Making a hotel spend money on labor costs to defend a charge that you know is 100% correct is not brilliant, in my book.