I think that just means that some faculty member is sponsoring you to have building access and a login account, more or less. (And the implications of affiliation of course.)
There's some less direct symbiotic benefits too, like the LibrePlanet has been at the MIT Stata Center for a couple years (at least). These sorts of things are facilitated by his role, for sure. I hope well-meaning conferences like that don't get disrupted by his resignation.
LibrePlanet has been at Stata through the sponsorship of SIPB, MIT's computer club, which has the ability to book rooms as a student group. Not through Stallman.