Clarifying: what you can do is "dispute charges." What the credit card can do is "reverse charges."

The credit cards work because consumers trust them. As such, credit cards will shit all over a merchant before they'll upset a consumer. They won't aid fraud, however. They've got an agreement with you and they've got an agreement with them and they've got verbiage in both agreements that says they're the final arbiter of all disputes but because of that whole "trust" thing they'll side with you if you can make a half-way decent case that you were wronged.

I've probably disputed credit card charges a half-dozen times in my life. They've always gone in my favor. The biggest one was a mechanic that charged me $1700 without fixing the problem; worse than that, they didn't hook my heater hoses back up so my car vomited all of its coolant all over Ventura blvd. and started overheating again. That one took a 3-page essay with photographs. The smallest one was against Radio Shack that refused to honor a money-back guarantee on a soldering iron that straight-up didn't light.

If you can copy-paste an agreement in which they expressly state they will do what they expressly aren't doing, the process moves at a brisk pace.