The therapists I have had (3 so far, as the clinical practice I use has some amount of turnover and one moved out of state) ALL have said in the first session that if I should happen to see them outside of the office, they will give absolutely NO indication they know me, unless I initiate. And that this is while I was in their care or and at any time in the future, even after I stop therapy with them.
They said it violates my privacy if anyone I may be with or even strangers just around know that they are a therapist and as a result would know that I know them — likely in a professional&client capacity. Some people, for very good reason, don’t want others to know they’ve had MH issues / therapy. Their interaction with you needs to be kept secret, unless you choose to reveal that secrecy. I imagine it’s linked to the HIPPA stuff.
It’s kinda shocking how this person doesn’t know or follow this protocol and might have out’ed you, even just with a smile.
Maybe you ought to show them what I just wrote?