I think my t genuinely cares for me within the therapeutic framework, and probably does for all her clients (or at least most of them). My T has super firm boundaries around her work and I can't imagine her ever having a friendship with a client outside of the frame of therapy though.
But, robust therapeutic boundaries do not exclude genuine care. Personally I don't think it is appropriate to have a relationship with a therapist outside of the therapy room. The therapeutic relationship is very much a one way one. It's that way for a reason.