I dunno...I think it was Asimov who said that SF "is whatever I point to
and say, 'That's SF.'" It takes place in the future, 250 years from now, on a
space station, with laws that don't exist at this time, in a context not quite
the present. To use your form of categorization, then there are many stories
in, for instance, "The Martian Chronicles" that don't qualify as SF. Also,
the solution to the G'Kar/Londo problem is a science-oriented solution that
can *only* work in space, using lightspeed as an aspect of the solution.

Anyway, I've always thought that the discussion of what was or wasn't SF
was kind of silly at the heart of it; like arguing over how many angels can
dance on the head of a pin (the answer to which, by the way, is "As many as
want to). Serling created the Twilight Zone, and Roddenberry created Trek, to
tell good stories that people could relate to. Some were more SF than others.
In some cases they simply changed the background of the characters from
minorities to aliens. The obligation of a writer is to tell a good story,
first and foremost, and let others worry abou whether or not it fits the
"rules" they have assembled for what is or is not SF...rules that will vary
from person to person to person.

jms

(Who just remembered that the other definition of SF is speculative
fiction...and speculating about the future of unions, and labor laws, and
government, and finance, is as legitimate as reversing the tachyon field to
better differentiate the hyperdrive system diagnostics.)