You can't mix up "public property" with "private property of a public entity." The former is something like a river--it's public property and you're entitled to swim in it and cannot be excluded arbitrarily. But the latter is the same as private property in any other hands. To the extent that anything would change (and I don't think anything would), it would not be because the property rights are in any way different, but because the actions of public universities are "government action" and might be constrained for other reasons.

Yeah, ok, makes sense. Thanks.