Any time there is a camera crew there, the location has been booked, release forms secured, plus security and possibly even police to lock the location off. As someone mentioned regarding the scenes of him writing, this stuff is regularly staged. I was a reality-TV DP for a few years and this is always how this stuff is done, just because you have to.
He probably does occasionally do something like this though. He drives himself around too, and takes his kids to school when they were younger, and I'm sure he does other "normal" things; it's not like he is a prisoner in his house. But it's not like the way you and I live. Mega-celebrities simply can't go about their business like us, although sometimes they try.