I must be missing something but doesn't the genny have an alternator to charge its starting battery?
I don't have an onboard genny in my trailer but I do have a genny onboard my boat. That genny has its own, independent, starting battery. That way even if the 'house' batterys are dead & the engine/s batterys are dead the genny can be started to charge them up.
Do RVs with gennys typically not have their own starting battery?