Question on inverter/charger AC backfeed

The inverter generally will have a transfer switch built into it, or associated with it. It doesn't send power back to the electric panel to power circuits; rather, there are some circuits that are connected through the inverter, and it either sends power from the electric panel on to them (when not inverting) or powers them itself (when inverting). Often they also have one or more circuit breakers of some sort on the inverter for these circuit(s), so you might have for instance a 30A circuit feeding the inverter/charger and a pair of 20A circuits coming off of it (which, naturally, could not be simultaneously loaded to 20A in this example).

Any system that backfeeds the electric panel is likely to be dangerous, as it would leave the shore power cord live when it's unplugged. A built-in generator with a transfer swtich is okay because of the transfer switch, which disconnects the shore power cord when the generator is supplying power; but if the generator is not running, the shore cord is connected to the electric panel and any power present there would be exposed at its plug.