Personally, I think that the group tests don't usually show a kid as very gifted if they're not at least mildly gifted but definitely miss some kids who are very gifted. CoGAT specifically says that they are not meant to test really gifted kids.
This isn't totally relevant to the point at hand, but I'm not sure that I totally agree on this for two reasons. I do agree that gifted, and particularly HG+ and 2e, kids can easily be missed on group tests.
However, I personally know two kids who've taken the WISC IQ test more than once and had clearly average scores both times save for higher than average memory and processing speed indices and both hit the 95th percentile in one area on the CogAT scores needed for GT ids where I live. We also see around 15+% of our local kids testing as "gifted" using that 95th percentile bar on the CogAT even in our district that isn't unusually high performing and which I'd be willing to bet a lot isn't populated with an unusual number of gifted kids. We also have a lot of test prep going on for higher achieving kids, though, too and kids whose parents want the GT id. I really do think that the prep can artificially inflate scores for bright or typical kids.
For really out of the box thinkers, I'm not sure if it would be as easy to prep them into higher scores, though.
