In my opinion, Rainbow's therapist (and all therapists) are responsible for their own boundaries, and determining if one is crossed. If one is crossed, the therapist then is responsible for and quite capable of (hopefully)addressing the concern. Boundaries are different for everybody, some people guard theirs vigorously, some are really lenient, and everything else in between.

In my experience, using obsession as a descriptor may be a part of the experience, but that is only the surface behavior (as was duly noted). In my opinion, focusing on the therapist and his/her availability can be due to an ambivalent attachment style:
"Unable to use caregiver as a secure base, seeking proximity before separation occurs. Distressed on separation with ambivalence, anger, reluctance to warm to caregiver and return to play on return. Preoccupied with caregiver's availability, seeking contact but resisting angrily when it is achieved. Not easily calmed by stranger. In this relationship, the child always feels anxious because the caregiver's availability is never consistent."

If a caregiver's availability isn't consistent, and (possibly) the child is sensitive, then the child learns to engage in proximity/attachment seeking behaviors to a marked degree because their behavior works at times. The child then becomes preoccupied because of the inconsistency, and attachment seeking behaviors become the end-all/be-all. This is true for various behaviors, that inconsistency results in an escalation of whatever the behavior may be. Unfortunately, paired with this, the child's/adult's sense of worth, sense of self, etc., are intricately tied into not having a consistent safe base. This, in my view, is different than an addiction although similar characteristics may be present.

I don't know yet how this type of attachment disorder or other types of attachment disorders are overcome, I have some hope that they can be, though.