The only thing that makes them "the big boys" is their football program. Without that, nobody would refer to them that way. Sure, most have big student populations, but there are plenty of big-time football schools that don't have big student populations.
So why should these school be referred to as "the big boys"? They are simple "one of the big boys of college football", just as UND, UMD and Denver are "the big boys of college hockey".