I agree the dealer is wrong stating that you can't test the generator when shore power is connected, unless the trailer has a very special transfer switch with a lock out that prevents the generator from being started with power present on the shore cable side of the transfer switch, which would only be found in a tiny percentage of RVs.
That said, it would be a sensible saftey precaution to disconnect the shore power cable before testing the generator, in case the transfer switch had a catastrophic failure that tied the shore power side and generator side together (very un-likely). Certainly if the shore power fails, and you want to fire up the generator, disconnect your shore cable. This might save the life of someone who thought he was working on dead power lines if the transfer switch failed and energized the shore cable feeding back into the trailer park electrical system.