At one role for a bank the mute button stopped the customer from hearing what you said, but it still went on to the recording.
Reviewing problem calls was always entertaining, since you couldn't tell, except by recall or lack of reaction, when mute was on.
One thing I did learn was that the people calling on the VIP* lines were much more respectful, polite and friendly than those on the regular lines. Even when someone had made a serious cockup, while they were very clear that while they wanted it fixed ASAP they did not consider me at fault, but rather that I was part of the solution.
The business clients were fine too. Since they actually used the system a lot they often knew exactly what they needed doing, or at least had a good idea of what the problem might be. Since 90% of things that went wrong involved payroll there was again the focus on solving the problem first, tidying up the resulting messes, then only doing the blame game to try and prevent things in the future. Also showed me that quite a lot of employers take their responsibilities seriously, so if a payroll batch failed halfway they'd run it again and pay some people twice and sort it later rather than risk anyone not getting the pay on time. Or when there wasn't enough to cover a full second run before overnight clearing deadline, so all the C suite and department heads pay got held back for a few days.
My ex works for the tax department. The list of things she's been called, either directly or on an unmuted phone, are far worse than anything I've had. Best is that it's in three official languages, plus whatever else the caller has. She's Dutch, so is pretty direct about it, so when one client said "oh, it's that cunt from the tax department" when someone in the room with her asked who she was on the phone with, when the client picked up the phone again my ex cheerily said "hi, it's the cunt from the tax department here, do you have that reference code now?". After sorting the client out, she even got a sincere apology, which is pretty rare here in the Netherlands :D
* private banking and share trading, people who would describe themselves as comfortable rather than rich...