Yes, very annoying. Our school had our DD take the CogAt at school even though she had already had private testing. She did well and then it seemed like all the magic doors open. It doesn't make sense to me, but the have their reasons. I won't comment on my opinon about the validity of the reasons, but it's more complicated than I first imagined.
My rec would be go ahead and have them administer their own test. I'm sure he'll do great on it and if not, cross that bridge, you know the rest........