Eh, sort of. A bunch of those smaller name schools around here are very subject-specific. Bentley is primarily a business school, Wellesley is all-female, Brandeis has the stereotype that it's all Jewish students (though it's not), Babson I don't know much about - but they all generally are not as heavily looked at as the schools in the city, for that main reason. They're not in the city, and that's where the prospective students want to be.
BU, BC, and Tufts are "fallback" schools for those who are shooting for Harvard, Yale, Brown, and other Ivies. I've generally found MIT students don't apply to the other schools around here. Place BU, BC, or Tufts by themselves in nearly any other location in the country and they'd be the top choice of that city. While being in the city with everyone else is all of the colleges' greatest resource, being in the city with everyone else also means they cannibalize one another. Still, BU found a way to convince 52,500 students to apply for this fall.
Place a Michigan, Wisconsin, Penn State, or any other highly ranked B1G public university in the state of Massachusetts, and they would end up in a similar boat to UMass, in that they'd be overlooked for the Boston schools. Very, very, very few Massachusetts high school students with the credentials to go to a school of the caliber that exists in Boston readily aspire to go to UMass. Sure, those B1G schools are better, but the stigma of being "State", and their reputation after competing head to head with the private schools would reduce their overall profile.