This is a good point. But if we're going to lay all the facts out here, we should consider a couple of things: (1) Gates doesn't own the home, and (2) I believe Harvard University, which does own the home, does not pay any property taxes on it as a non-profit institution.
If Point (2) is correct, then I think it says a lot about what happened here. Taxpaying citizens probably have far more respect for the people who work for them than do those who don't pay taxes at all.
I understand this point but if we go there then the person who is merely renting and people in Gates' position with his home don't get the same respect for their privacy as a private home owner. I think the idea is not so much to protect the property owner as it is to respect a person's privacy. I think a rented apartment should be viewed with the same respect as a privately owned home (provided no conflict with the property's actual owner is in play). In practice, this is Gates' home and I would imagine he feels like he has a right to expect a certain amount of privacy even though it is a university provided pad.