Well... none of it is really private property per se. The MBTA is a public entity running a public service entirely financed by the public and its customers (who are also the public). Moreover, these fiber "closets" aren't even closets and anyone who has had any networking experience at all would be rather appalled just walking around the T-stops. Most of the break-out boxes are either wide open or unlocked and are not even secured behind a door. At just about every stop you can find a fiber "closet" mounted on a supporting strut in the middle of the station.
To the other person that replied to you though. The MBTA system most likely didn't belong to the MIT students at all since I very much doubt the majority of them were even from the Boston area.
Either way, the MBTA system is stupidly easy to circumvent and with the amount of fiber they have running throughout the T they really should've built a more reliable system. The buses and commuter rail could've been covered too with either a radio or satellite based network (which is currently in place on most MBCR coaches).