Msever, thanks for those answers. They were helpful. They further confirm what I believe is the problem - your automatic transfer switch (ATS)
An ATS is usually a stand-alone device, and the ones I've seen were installed near where the shore-power cord goes into the RV, but who knows. The ATS detects if A/C power is coming from either the generator or shore-power, and automatically switches to the source that's providing power.
When you asked the tech if the problem could be with the generator's ATS, his answer was technically correct, although somewhat incomplete - your generator doesn't have an ATS - the motorhome has one. I can't help but wonder if his answer was intentionally worded that way to confuse you, but you'll have to determine that.
If A/C power from the generator or shore-power can't get past the ATS, because it has malfunctioned, you would see exactly the symptoms you're having. I am no expert on your inverter, but from what you've said, it seems to be working. It's inverting 12 volts D/C to 120 volts A/C and powering your outlets and appropriate appliances. Maybe the tech has determined that another of its functions isn't operating properly, but I don't know what that would be.
If you don't feel comfortable locating and testing your ATS, my recommendation would be to take the RV to another tech and get another opinion. Or, call a mobile RV tech and have them come to you. If they've been in business for awhile, they should be able to resolve this fairly quickly. An new ATS is a lot cheaper than a new inverter.
Keep us posted.
Kev