I don't really see this as an issue about googling her therapist. I see this as an issue about respecting another person's reasonable boundaries. Rainbow, you directly asked for information about your T's boyfriend (not your T), and your T declined to give you that information very directly.
This isn't about your T. It is about a private citizen associated with your T that you feel you should for some reason have right to information about. Your T has a right to protect the privacy of friends and family.

I personally don't think any of us have a right to invade the privacy of therapist's private associations, and it is rude to say the therapist has responsibility to protect not only their own information but also the information of anyone associated with them. Who can honestly really do that? In this case, the therapist is trying to do exactly that and is still being criticized.

I've seen people here who have gotten info by pretending to be someone else, by going through friends and relatives and children . . . At some point, a sense of basic respect for others' privacy should prevail over primal curiosity and sense of entitlement to know all -- a sense of basic manners and respect of boundaries should kick in rather than excusing all lack of respect for others under the excuse that everybody does it or if it is out there it is fair game.

Just because you can doesn't mean you should. Rainbow, you already know that or you wouldn't have made the original post. Use your sense of right and wrong here. That is the respectful and adult way to approach this.