Probably I should drift back off and bring closure to my little game.
The other two schools I was thinking are The Pennsylvania State University and The Johns Hopkins University. As cited near the beginning of this thread, people often include the "the" and pronounce it "thee" for emphasis. I think it's done by non-OSU people as a light-hearted mocking of the name. OSU people might say it in the spirit of distinguishing themselves from other, peer schools, or as the school in Ohio (implication being the Ohio is a superior state). All in good fun as far as I'm concerned.
I don't think I've ever heard Penn State adopt that mindset but maybe they do. I've heard some academic types refer to JHU in a way similar to OSU, only from the academic prestige point of view. It is, after all, a highly regarded school.
And there you have it.