A couple things:
1. You don't need ownership to have rights related to privacy or control. You don't have to be a homeowner to have a right against people invading your home. The hackers who started the free software movement were not primarily computing on devices they personally owned.
2. Personal ownership of computing devices is not necessarily what the term 'private property' refers to. Personal ownership of computing devices is very much possible without private _property_: https://en.m.wikipedia.org/wiki/Personal_property#Personal_v...