why? are the gennys in RVs different in that they can run microwaves somehow?
Fair point. I'm sure some of it is my paranoia talking. Also, don't RVs also usually have smaller (size and power) appliances and very often have soft start kits on the ACs, etc? That being said, google is loaded with people complaining about RV microwave power while on generator, and most RVs are designed to work best on "shore" power. In years past, better RV generators were 1800 RPM 2-cylinder synchronous, and were way under-rated (or to be more fair, most "emergency" generators are way over-rated), with lots more "starting" capacity (i.e. subtransient reactance), since they were designed for continuous use.
Anyway, I'm not saying it won't work. All I'm saying is, microwaves push the envelope more than most other appliances when it comes to small generators. In terms of failure to work, as well as causing damage to themselves, the generators and anything else that may be sensitive and plugged in at the wrong time. It's a risk I'd rather live without.
Now at work, on a megawatt generator, I don't have any concerns about the microwave. But even so, half a dozen failed capacitors in the wrong place will make more than enough noise to re-create the OP's UPS running on battery issue. BTDT, and chasing them down was lots of fun. To be fair, we're talking about caps the size of shaving cream cans (maybe twice the size of a central air compressor cap), but for 600VAC caps, that's still not a lot of capacitance.