I used to be a telecommunication tech. A number of times I would get annoying calls in the middle of the night. More than once I would get a call from some hotshot who was making a call and heard static and wanted me to come and fix his phone system right away. I would tell them, "People get static all time. It could have been a bad line. If you want I can open a ticket and we can send someone out in the morning." Sometimes they would insist that they never heard static on their line and tell me I had to fix it now. I would tell them I wasn't coming out. If they threatened to call my boss, I would tell them to go ahead. My boss always supported me especially if the same person woke him up at 3am.
I wouldn't take personal abuse from clients no job was worth that to me. There were times when I told the client to call us back when they wanted to respond civilly as I walked out the door. Never got fired for that.
There were times when I needed to fix the client instead of the phone system. There were times when someone didn't know how to use the system and insisted the phones were broken. It was difficult sometimes to get them to listen but if I was patient and they were too I could spend the time to explain how their phone worked. Unfortunately I got a reputation for being good with the clients and was often selected to visit "problem" accounts.