No - I can hear people in other offices at work, or talking in the halls, but never in a medical office or therapist's office.

At work it can be distracting, but I'm pretty good at tuning background noise out if I'm in a focussed mood.

Do other clients of his complain about the noise? Is there any other part of his space where you could meet? Could he borrow another office for your sessions? Does he do weekend sessions or do the people next door take a lunch break and could you schedule with him then?

Eta: if you can't make out most of their words, they probably can't make out yours, either.