A few points:
GA autopilots do not have redundancy, and most have poor error detection, and they can and do fail. I've had many autopilot failures, and this is the most modern Honeywell KFC225 type. So while an AP is a great safety aid (through workload reduction) one does need to keep an eye on it, and know where to disconnect it. The red button is not enough: I've had one failure where the red button didn't disconnect, and one needs to know where the AP master switch is, and/or the servo circuit breakers.
If one has a flight director then one can use the AP for that even if the servos are burnt out.
Most PPL-level instructors are clueless about autopilots and most other forms of "advanced" avionics. One is just as likely to be told a load of bull. So one needs to choose the instructor carefully. All will speak with confidence, but only some know this highly type specific stuff.
Whether an AP should be engaged upon loss of control in IMC is debatable. I'd like to see a reference for the FAA guidance reported - it must be type specific. An instrument pilot must know how to do (partial panel and full panel) unusual attitude recovery in IMC. If one's vac pump goes, and you have a vac horizon, and the AP happens to work off that, then engaging the AP will do no good. You have to recover manually, and will be doing it partial panel too. That's why one must understand the particular installation. Also any modern AP will auto disconnect of bank or pitch values exceed X degrees, say 20 or 30, and will thus disconnect in serious turbulence.
One should use an AP all the time conditions of actual or potential heavy workload. Always engage it if you have too much to do. Then you won't get into a loss of control situation in the first place.