You're argument holds water, but the problem is when we start getting into OS's that actually don't ship any of the GNU userland. The classic example is Alpine Linux. Do we call that BusyBox/Linux? WSL 1 was a super weird anti-example where Microsoft skipped out on the Linux and shipped GNU stuff and still called it Linux. I think the colloquial naming convention became something like Kleenex or Google where we default to blowing our nose with (generic usage, not brand usage) "kleenex" with off-brand tissues or had our parents (generic usage, not brand usage) "google" something on Bing (as thats the default search engine of Windows).
Depends on what you mean by Linux. The ABI Microsoft were attempting to emulate was absolutely Linux. (This API business is exactly the issue with Oracle vs Google over Java).