You ask an interesting question Fred.
Yes, every PC made in the past 10-12 years has a power transfer switch. It is a gray electrical box, maybe 8" x 8" x 3" tall, typically located in the house, just above the generator. At least that is where ours is, inside our no-slide front dinette bench seat.
Now you have me scratching my head too......When on pole-power or generator-power, the outlets inside get their power from those two sources via that power transfer switch. But how 110v from the inverter is disabled, I don't know. Maybe it's all common, 110v coming from the power transfer switch being back-fed into the 110v output of the inverter.
ADDING: Oh, I see Barry has an explanation. He beat my reply by seconds. So the inverter has the smarts to shut down it's on 110v generation when being supplied by another source.