As far as privacy is concerned, there's not much difference between using someone's browser and inviting them into you home. Imagine two people show up at your door. One is your trusted friend. The other is your landlord's friend, and you don't trust them.
Would it be a big deal for your landlord to push his friend in the door when you try to let your friend in? After all, he owns the home (you just pay for a license to use it), and he trusts his friend, so why should you care?