POSIX isn't actually about operating systems. POSIX (1003.1) is about source-level compatibility for 2 languages: C99 and shell scripts.
If your C programs use only C99+POSIX facilities, and your shell programs use only POSIX features and utilities, and they work on a platform, then that platform is eligible to be POSIX certified. POSIX doesn't care about the kernel or syscalls or anything like that. It cares about libc, libm, libl, and a couple of file paths.
Actually to a certain extent, I think one could call POSIX the actual C runtime library.
As C runtime + POSIX calls (I know it didn't exist back then) is what defined C when it was still UNIX only, but ANSI didn't want to make the language standard that big.
Linux is just the kernel. Distributions should certify. And I do not see anyone going fot it. There is at least one distribution posix certified: Inspur K-UX.
The equivalence in linux land should be LSB, which many distributions certify to.
It's POSIX certified. Linux isn't. That should tell people quite a bit about POSIX, but it never seems to...