Since we didn't handle billing, I had to call AT&T with the customer on the line and talk them both through the process of removing the charges(AT&T was feeding customers a line about not handling billing either, for some reason). After doing it a few times, I realized I could do it without the customer, all I needed was a name and a phone number.
It never came down to impersonating the customer, instead, I would just say I was calling on behalf of a customer. Once, a call got escalated to a higher support tier, with the miscommunication that I was a VP of a partner company, which made the agents more responsive, making the process easier, so I just kept reusing that line.
Eventually, I just asked, "what do I tell the next agent I have to deal with so we can just bypass all the lies?" (regarding their inability to modify billing charges). This was happily given to me, and I could now call AT&T support and say, "I'm calling for user X with number Y. I need you to go into the tool and click on Z and then remove the charge from such and such service." Again, when delivered with authority, the rep would do it, no questions asked.
It's hard to fault them, I probably would have done the same in their position. Still, it's scary knowing how little it takes to get customer service to reveal/modify things without hard verification.