From a neutral point, it looks like they are probably willing to do something for you with proof you were charged. Most credit card companies don't penalize or charge interest on disputed amounts once filed. I do agree RF's support staff is undertrained and generally useless. I have always received good results from Tim Shor though. I believe he's more than administator, and more likely the owner.
I don't doubt their was a problem on their end, as I've had several problems with their scripts myself, as well as about every other registrar I've dealt with. But, just because their database shows a charge, doesn't mean the problem isn't with their database and was ACTUALLY charged to your credit card. It could be a glitch, or someone elses card credited to your account.
BTW, Good luck with luxorhotels.net. Sounds like an invitation for a C&D letter to me. I wouldn't take on the Vegas casinos and their unlimited sources for anything.