I'm doing the "it's still a 'public service' even if there are location restrictions" argument, since almost anything I can think of as a typical example of a "public service" (police, fire, medical, education, access to courts, etc.) also have location restrictions and we call all of those things "public services".

If you want a special definition of "public service" that means "accessible every human on earth without any exclusions" then that's fine, but telling someone something isn't a public service because you want to use a special definition of the phrase that no one else seems to use is a bit... overly argumentative?