IMHO, they would be perfectly justified to call the diver on this if they were that hard-ass of a shop. Their compressor, their rules.
@abnfrog teaches an exhaustive and comprehensive 'hands-on' VIP Inspector course. He knows that his card should be good anywhere, so do I. But how would any shop know that every other instructor does the same? How many times have we heard on this board "It is the instructor not the agency"?
Edit: Life is full of compromises, this is the only reasonable way to resolve this issue (that I can see).
And, continuing with the hypothetical, if the "instructor not the agency" is what a shop finds compelling, then why does a shop honor just about any agency's card in filling the cardholder's tank? Is it because, in the case of a VIP card, they figure that a poorly trained cardholder puts the shop's fill person at risk, but in the case of a c-card for diving, they figure that a poorly trained cardholder doesn't put the shop's people at risk? I think that is exactly it. Once again, we have an example of how little weight holding a dive agency's card carries in the real world.