Tesla says never to charge off of a generator, too.
And in many cases they are correct. But it's because the waveshape out of some generators can damage the chargers used in EVs. Some are much better than others. Some HFT generators I would not use for anything other than lights. But I checked the waveshape and frequency of the Onan generator output in my RV and it is a perfect sinewave and at 60.0 hz until 3.5 KW where it slows down a bit, but that is its max spec anyway. So I use it to charge my Zero (up to 2.4 KW) without issues during many of my RV trips in locations where there is no other juice. I would never just connect a Zero to a generator without checking the waveform & frequency first. Tesla writes their manuals for the average non-technical person, so they will simply say do not do such. But they also realize that those who can and know how to check a generator output waveshape will know to ignore such info from Tesla or Zero, etc. if it checks okay, as mine did.
BTW, Tesla has their own portable diesel generators to charge Teslas with. They used to have a temporary one or two on I-5 on a very crowded weekend to have a couple of quick extra charge stations where they thought they will probably be needed. The gas companies and other anti EVers loved to make a big joke out of that!
Also
see here.So even Tesla themselves charge their own cars via generator. But no doubt they are as clean as can be. But perhaps the L3 don't even count as that is DC anyway. But it's okay to use a clean generator on L2 (or L1) as well, as long as the waveshape is about as clean as the AC in your home.
-Don- Reno, NV