How do you define "a real test of their capabilities"?
While we start the hour long skills test off with some fizzbuzz weeders, we quickly move into harder questions pulled out of issues we've resolved in the real world that are likely to be of the same shape of future work.
If people are offended by fizzbuzz, they don't express it often during interviews/employment/exit interviews. The most common reaction from someone who can solve it is a bit of a wink and a nod as they slay it and move on to the "real" stuff.
I've never had anyone ace our test. No one is a 10 everywhere. I think there's a lot of value in how you approach things and react to a blocker or limitation. We watch this closely too. It isn't just about saying "Every answer is correct, so hire me".
Lastly, we're out of Houston, TX. I'm guessing the culture is very different in CA and perhaps that's the mismatch.
For what it's worth, I'm a native Texan out of Dallas and wouldn't dream of giving someone with demonstrated development ability, like OP has, a fizzbuzz "test" as part of hiring. I'm guessing the culture is very different in Houston and perhaps that's the mismatch.
In that situation I think a fizzbuzz test is a bit strange.
But, it's your company and I don't think anybody should tell you how to run it, I was just curious about why you'd administer this particular test on someone that should be able to not only ace it but will likely be insulted by it.