Yserbius, that is not true. Most of the time there is no OU mashgiach at production time. If there is one, the heimishe hechsher doesn’t automatically rely on him, it depends on who he is. If he is someone they feel comfortable with, then yes, they’ll just rely on his being there and decide they don’t need to do anything more. But if he isn’t someone they trust so much, then they’ll send their own person.
I do know one person who was supervising for the OU when a heimishe rov walked in, took one look at him, and said “if you’re the mashgiach here then I’m sure everything is good”, and walked straight out. He thought this meant the rov was not doing anything to give his hechsher. I pointed out that he had done all he needed; he didn’t just rely on the OU, he went out there and saw who was in charge, and that is very valuable information for those who rely on his hechsher.