What do you mean "the kind of private property"? Private property is private property. MIT is a private university and its campus buildings and its campus network is private property.
The fact that it's an educational institution doesn't make its property any less private. IIRC, the fact that MIT is engaged in interstate commerce with the public brings it within the domain of the Civil Rights Act of 1964 and the Americans with Disabilities Act of 1990, but those laws carry only very specific limitations: MIT can't refuse someone access solely based on their: race, color, religion, or national origin, and must make reasonable accommodations for people with disabilities. Those regulations on the use of MIT's private property don't make the property any less private than any other such regulations, nor do they in any way prejudice MIT's rights to control access to their property for any other reason.