I've experienced both a T being nice about referring me on in that way, and a T genuinely being concerned about where I was headed so she wanted to make sure I had adequate support & expertice around.
A T has a duty to make sure you are getting the care you need and deserve. Depending on T's working environment (one of the T's who referred me on did so b/c she was restricted in what she could offer by the clinic policies), she may well just want additional support around for you. The T I had (and am returning to after I move) who wanted to make sure I was supported continured to see me while I was also attending a specialized program. Even if insurance had denied payment, we would have worked somethign out so that I could keep seeing her... My most recent T I believe would have continued to see me if I had been seeing her elsewhere. The clinic through which I received services has relatively strict guidelines around what they can offer a client. T said that she would have liked to keep seeing me, but clinic policy restricted that. I am choosing to believe she was genuine when she said that.
I think a lot of the time we read into things based on past experiences. I tend to think most people hate me and would rather me be gone. I read that into T's words and actions a lot, even when it's the furthest thing from her intentions... T and I had a few conversations around being genuine and meaning what we say (both on her end and mine). Maybe you could have a conversation with your T around whether or not she is being genuine? It may just be that she feels you need more support that she can provide by herself at this time. She may be willing to keep seeing you while you also get services at the other clinic, or be planning on you returning to see her (if there is some conflict around "duplication of services" if you were to see both her and someone at the clinic). I would recommend asking though.