I must agree with PanchoPippin. In the absence of some other defining achievement, the school you attend will be a proxy for your intelligence and authority on various subjects. Even late in one's career, she is often introduced at public speaking events as a graduate of such-and-such business school. People need a reason to pay attention, and your alma mater sends a signal (however subconsciously) to tune in or tune out.
OP, ask yourself this: If you were looking for the most talented young professionals, which business schools would you visit? There are simply too many nooks and crannies in this world to look everywhere, so recruiters have to draw the line somewhere. There is an underlying assumption that a rational applicant will show preference for higher-ranked schools, and the success of our applicant-school matchmaking system would fall apart if applicants didn't do this. Therefore applicants should apply to a range of schools, and it is in the best interest of both applicants and recruiters for applicants to matriculate at the "best" schools they get into. After all, schools can't control who applies. During the three phases of the application process (selecting which schools to apply to, admitting students from applicant pool, selecting which school to attend), agency shifts from student to school and back to student again. If you decide now to attend OSU for your MBA, you're opting out of the whole process. I recommend at the very least applying to a few other schools.
EDIT: I myself went to a large, economically convenient state school. I regret it. Everything in this post occurred to me after the age of 23.
PanchoPippin, perhaps you could add something to this discussion by explaining why you chose Tuck over Kellogg and Booth? Were there financial or social considerations?