My doctor would so be like that with me; she is so protective with my medical concerns, she gets on me all the time lol. I told her that I started seeing a counselor after my mom passed (she doesn't know there is so much more to my history) and she always asks me how I am doing and says that if my counselor ever diagnoses me with anything she would love to know and be able to talk with my counselor to keep that congruent with my medical aspect. I don't think it's necessarily a dual relationship, all doctors are different and some would never be like that.