Just because it meets their specs won't guarantee that it's any good. According to Columbia's website, the HPVA thickness tolerance is +0, -3/64".
We do a recurring job that uses about 40 sheets of red oak plywood. I buy from 3 different manufacturers. None are really all that great. I find that plywood with a poplar core tends to be a little better than some of the others. But the real problem that I see a lot is de-laminating of the face veneers. Splintery woods like oak are the worst offenders.
Personally, if I were buying plywood for personal projects, I'd by the Purebond Classic Core. I've used it and it's nice. A major benefit is that it tends to be a lot flatter than regular plywood, which is nice for vacuum holding.
It looks like the J classic core is a more consistent thickness, based on their website.