I would be very bothered by this situation. I would feel that the receptionist intrudes into the place between me and my T without being invited. I don't appreciate such fake friendliness (but I'm not from US either - I'm from a cold European country where such friendliness between (half)strangers is not norm).

My T situation is completely different. It's a private practice and there is no reception, the waiting room is only for one person and when I'm leaving I'm exiting through another door that doesn't go through the waiting room. So, when I hug with my T (it happens sometimes) it always happens in the consulting room in the privacy of two of us. I wouldn't want to share this with anyone else, neither would I want to see my T hugging someone else (I actually doubt he does).

It just seems strange to me that a receptionist in a psychotherapeutic practice is so careless with her comments. Shouldn't she know that the psychotherapy relation is a bit difference than a relationship with any other clinician? Would you actually prefer to hug your T in the consultation room? I personally don't see anything inappropriate in that.