I think the warning you might be thinking of is that a breaker can fail to pop if an inverter/generator is on the same circuit as a high wattage device. Since some energy would go directly from generation to device, the breaker will only see the “net” energy consumption. So if the generator puts out 1500W and the device decides to draw 3000W, a 15A breaker only sees 1500, and won’t trip even though the device is pulling way too much. If the breaker was sized for the wiring, then the wiring to that outlet could catch fire due to the breaker not tripping. That’s the main reason I know of why a generator or inverter should be on a dedicated circuit, to force the energy out one breaker and in another, so that the breaker can see an accurate measure of energy and trip when necessary.
I think the warning you might be thinking of is that a breaker can fail to pop if an inverter/generator is on the same circuit as a high wattage device. Since some energy would go directly from generation to device, the breaker will only see the “net” energy consumption. So if the generator puts out 1500W and the device decides to draw 3000W, a 15A breaker only sees 1500, and won’t trip even though the device is pulling way too much. If the breaker was sized for the wiring, then the wiring to that outlet could catch fire due to the breaker not tripping. That’s the main reason I know of why a generator or inverter should be on a dedicated circuit, to force the energy out one breaker and in another, so that the breaker can see an accurate measure of energy and trip when necessary.