Did you just ask "do you accept American Express for charging?" or did you give the whole convoluted story that you described in your original post? Because honestly, I had no idea what you were trying to ask from your original post and I can understand how a CM would be confused by your question if you phrased it anything like your original post.
Remember, although you're excited about your vacation and want to share even the minute details with everyone, sometimes it is best to just ask the direct question instead of giving the backstory along with it. "Can I use my American Express card at my resort?" is a direct, simple question which should elicit a direct, simple answer of yes or no.
As far as the CM "hanging up" on you, I think it is more likely just a slip of the hand. Despite what some people think, it isn't a training issue, some people just aren't as perfect as others

and do make occasional mistakes. Especially if CRO has a computerized phone system. I've worked on systems where the phone directory for tranfers has a button located adjacent to the call release button. Someone bumping into your chair as you were clicking your mouse to pull up the directory could cause your hand to slide just enough to click on the release button by accident. Heck, most of the CM's work in Florida and even though I've also lived in Florida for a few years, I still flinch when a roll of thunder claps directly overhead. I can easily see accidents happening but then I try to believe the best in people so I tend to be more willing to chalk something like that up to an accident rather than a deliberate action.