If they are good I don't see a true distinction between thinking and winging it. The thinking-on-the-wing is like someone said a good improvising for each situation. So yeah they learn the basics, but they if they are loosened up and ready to go with you they are thinking and flying at the same time.

In my particular case my therapist knows how sensitive his patients are to everything so he is quite careful and thoughtful but not to the point of not being spontaneous. In fact it is that spontaneous responsiveness that works the best for me. That comes from years and years of experience, in my opinion, though some might have a special gift for it.