A Rav hamachshir has the authority to set any conditions he wants. If the business owner doesn’t like it, he won’t use that Rav.
However, those who feel the hechsher is on the establishment in total now must require any business or establishment (linen store, doctor’s office, baseball stadium) to acquire a hashgacha. After all, if the hechsher is on the “atmosphere”, then any place with an atmosphere needs one . For anyone who thinks this is outrageous, it is being done in Bnei Brak,with more to come.