Perhaps the best way to handle this would be to make it very clear from the beginning that there might be students and ask a new client if s/he allows it or not. Then it is not a surprise. I don't think that bringing in a student out of the blue is a good idea in therapy for the client, but students still need to learn somewhere and shadowing real procedures is a good way of learning, IMO. I don't think that classroom or simulated experiences can do the same. I very much agree with Myrto that many people would not decline when they are put on the spot suddenly, both at the doctor's and T's office.

What I personally find more disturbing is when Ts who teach discuss their clients in the classroom, in way to many detail, without anyone ever having access to the full reality. They argue that doing it anonymously and changing some identifying details is fine. What is not fine, IMO, is how these anecdotes can be distorted by the presenter to fit whatever agenda they have. I know they do this a lot because I see it happen in relation to my own work. Then, I think having students observe sessions is a much better source of training.