Ok from the little bit of reading I've done, a few issues with generators:
1. Neutral and GND should be tied together via resistor, if the generator doesn't already do it. This is a common problem with L1. You can build or buy an adapter that does this. The EVSE will check that GND is actually connected (there should be a voltage potential between hot and GND) and fault if not.
2. Inverter generators preferred but, I've yet to see any solid tests demonstrating this beyond your typical forum conjecture & tall tales. Makes sense in theory, just not sure yet. Concern seems to range from changes in AC frequency (not sure that the charger's AC-DC converter would care) to spikes in voltage (depending on the frequency of these spikes, that could trick up the internal DC boosting circuit, at worst possibly cause erratic charging of the battery cells). True sinewave inverters tend to run on the small side, so Level 1 only, and 240V probably needs a traditional generator with a double-conversion UPS which is heavy and several thousand $$ for a 4+kW unit. I'm imagining what it would take to outfit a towing service with an on-the-fly EV charging solution, since they'd be the only ones to afford such a rig.
However, I'd guess #2 isn't as big an issue as people make it look.
3. EVSE would tell the car to pull full current during charging, but the genset might need some time to "ramp up". Not sure how the Ford actually deals with this, I'd imagine it "ramps up" the power draw over a minute or so but it would be nice to have a special "ramping" EVSE that could enforce this via the J1772 square wave's pulse width (stepping from 5A to 12A over 3 minutes or so). Teslas don't have this problem 'cause the charge rate can be manually set from the dashboard tablet UI.
2017 Ford Focus Electric (Magnetic)
2017 Ford C-Max Energi SE (Kona Blue)