Now I really tend to agree with your perceptions and feelings more than his strategy, and my parents (or anyone) never treated me that way. I mean, come on... why to make such a fuss about a pack pain that is extremely common in people?! My second T also had a back issue and eventually underwent surgery for it, although that was after I stopped seeing him in sessions, but told me that he had a back issue that troubled him very early on, once when I commented after a session (via email)that he seemed unusually disconnected that day. He responded immediately because he was very tired as his back pain disrupted his sleep the night prior. That was very easy to understand and it never even occurred to me to ruminate on it any further, just said something along the lines of "I am sorry, hope your back will get better soon". He told me about the surgery many months later, also in an email, when I inquired whether he would be available for a session after I no longer had regular sessions with him. Again, there was nothing weird about it and it did not make me preoccupied at all or make me fee I wanted to take care of him, but perhaps you are different in this sense.
In any case, if the same things happened to me, I would also definitely comment back to the T that it was completely unnecessary and please next time be as direct as he usually likes to be about other things - it will save a waste of time and energy. Perhaps some Ts (especially those who are more psychoanalytical) would see this as an opportunity to explore stuff about the client but your T does not usually come across to have that type of interest a lot. It really more sounds like he is primarily insecure about his health issue rather than anything else. People tend to hide insecurities and discomfort and sometimes project it onto others, make it sound like they hide to avoid discomfort for the other person. It can be BS sometimes