Both St John's and DePaul are Vincentian schools. They also were exclusively commuter schools (no school owned housing or residences on campus) until recently. Where they differed from other commuter schools is that their student bodies (in each case from major US cities with significant public transportation infrastructure) commuted via public transportation, not by driving to and from campus.
It wasn't until the early 1990's that DePaul built any on campus housing and it was nearly a decade later that St John's did. In each case many who followed each school felt that this damaged their basketball programs as once there was on campus housing, the schools could no longer provide a stipend (in lieu of housing) as part of the athletic scholarship. City kids could remain home and bank the stipend while playing at those schools.
As far as the other BE schools, I cannot speak for Butler, Creighton, Marquette or Xavier but with the exclusive, pricey eastern members (Georgetown, Providence Seton Hall, Villanova) very few underclassmen live off campus. The model they utilize, the students who do live off campus (I imagine fewer than Kolumbo is suggesting in his post) only do so as upperclassmen.