One of the most valuable skills you can have is the ability to react professionally on the fly. In appointment-driven businesses like ours, there is always the potential for confusion and misunderstandings, which sometimes results in a client being present without a trainer. Whether you are green or seasoned, you should be able to quickly look at a client's file and step in and give him/her an appropriate and solid workout.
This can feel intimidating, but it is essential - especially if you work in a studio or smaller facility. I have had to fill in many times for absent trainers, and I expect all trainers who work for me to have a familiarity with all studio clients so that they can do the same.
Don't get locked into the idea that you serve only your clients; you should be able to serve anyone at any time because you're that good at what you do.