A lot of people don't seem to realize that the internet is a public place.

If you run around naked on the street or are arrested while setting fire to the shop's Christmas tree, and T walks by and sees that, you'd expect him to mention it during the next session and you probably wouldn't be offended he did so. But if your T sees that on Facebook, people are suddenly offended? I don't understand that. If you don't want the T to see your Facebook, either adjust your settings so he can't (I don't have Facebook, but I think it's possible to do that) or cancel your Facebook page or don't put those things on Facebook.

I do believe however that if the T says "Hey, I ran across a post on Facebook about you setting a Chrismas tree on fire" or "Hey, I noticed you running around the marketplace naked last night.. you alright?" and the client says "Back off" or "I don't want to talk about it (right now)", the T should.
If he's worried about the safety or the client or those around him or the safety of innocent Christmas trees, he can say "I'm worried about you. I'd really like it if you'd talk to me about this to reassure me. Otherwise I might have to call for an assessment." (By 'assessment' I mean when they call someone who will evaluate whether you need to be hospitalized against your will)

I think I'm digressing.. I think this thread was about clients looking up the T. But it goes both ways, I think, although the T has more of a right to pry than the client - but both have the right to peruse the internet. And if you don't want something to be read by everyone with WiFi, don't put it on the internet.