I don't doubt your ability in the least, in fact I wouldn't be surprised if your physical skills far exceed mine, and plenty of other people's on here. It sounds like you are in great shape, and well trained and skilled in more than one art.
However none of that is remotely relevant on a forum
, even with video. Since we cannot actually (most of the time) train with one another in person all we have to go in arguments in the other person's words.
I don't think you've been intentionally dishonest, but I do think that you are succumbing to an MA marketing mindset where you are required to claim you art is somehow all-encompassing by doing things like claiming cross-training is not cross-training
Bottom line is on a purely academic level none of these arguments about groundfighting in kata seem to hold water. That doesn't mean that your blend of wrestling hasn't made you Karate more complete, I can certainly accept that, but it's not something that can be proved in written form on a forum.
That's the frustrating thing about forums, it really isn't
about what you can "do" on them, unlike actually training. It's just about what you can write and that's it.