Can you give some examples of what the fictional T says, and maybe the name of the book? The author could be "making up some of the statements". Or, like you say, it depends on the T's style and orientation. I'm guessing the fictional T shows more warmth and closeness than you get from your T. Please correct me if I'm wrong.
I've experienced wanting my T to say some of the things from, I'm sure you've guessed it,

Torey Hayden's books, which aren't fictional, but written in a fictional style.
I'm really interested to know what the fictional T says!