Can a client sue for mental injuries?
I am sure they could. I also believe that for a good trainer, there should never be a base for such a suit. I can only imagine this to come from a mentally unstable individual who is looking to sue somebody for something.
Difficult to imagine such a scenario in reality. I believe if I were to be suspicious, I would make sure only to train this individual with others around.
Ultimately, regardless how unfounded a charge may be, our reputation is one of our greatest assets as trainers.