I have to wonder, do they ask a brand new patient that? And then tell them they can't come in if they haven't had it? Do they ask to see proof of vaccination from the previous Vet? What are they going to do, run outside to shoot a poof of stuff up the new dog's nose and tell it to come back in two weeks? Where were they going to have you set your feet till your pup got it? I looked up recommendations on the time it takes the poof to be effective and came up with 2 days to 2 weeks.
If you and a friend have time to spare you could test that out. A phone call from a prospective (fake) new client might be all it takes.