When is it worth saying it's Linux? (The H)

Where do you think the LSB got their "standards" from? GNU, of course.
GNU itself was emulating Unix (GNU's not Unix!) but the particular
feel of the LSB was set by packaging choices made by distros on top of GNU. It
goes beyond merely Posix.

As for naming, of course it's political. But politics isn't merely advocacy -- it's also
about history. There are facts in politics. And as in history, one seeks to
understand where false histories arise, and in whose service.