Aaq, hashgochos rely on the owner only to a low degree. He’s not the Mashgiach. He doesn’t verify labels, etc…but having a frum person around can remove the need for a Mashgiach temidi, vis a vis basar she’nisalem min ha’ayin, and other such concerns.
Not allowing people to sell food without hashgocha is mentioned jn the achronim, because a ln owner is nogaya bedavar. But for some things, as mentioned, there’s room to be meikil.
Ths OU doesn’t hold of it, and requires a Mashgiach temidi in restaurants.