The UNIX specification is not the same as POSIX: https://en.wikipedia.org/wiki/Single_UNIX_Specification.

You might say "their exact view of what UNIX is isn't important and POSIX is," but POSIX is not the UNIX spec. You might think the Unix spec isn't important - and it really isn't today. Linux generally targets what is important and what users care about - and that isn't the UNIX spec. It is often the same as the UNIX spec, but not always and there are deviations.