Star Trek and Star Wars are part of pop culture. You don't need to have watched either of them to know what the Enterprise is, or who Luke Skywalker or Captain Kirk are. The SGC is part of the US military, not NASA.
I understand that, the SGC was part of the US Military in the world were NASA existed. And in a world where the general public knowledge of space exploration included the space shuttle as its peak of manned spaceflight technology. Hence it is probable that since the shuttle test bed was named in part for a TV show's vehicle that the said TV show, as a TV show, is part of the Stargate fictional universe