I once asked a trainer what he was trying to accomplish with his clients. He said, “I'm there to get them stronger and to improve their health.” I told him I didn't need him for that. I can buy running shoes and head out the door. I can go to gym and pick up weights. He countered that he was there to teach clients how to exercise correctly. I came back with the fact that anyone can go to the bookstore and buy any number of books on how to do it correctly.
I don't know what the role of a trainer is in other systems or gyms. There are several ways of approaching it. My thoughts on the subject have been shaped by my interactions with clients. A client once told me I come here to get a workout I could not get on my own. She said, “If I can do it on my own I don't need you anymore”. That really stuck with me.
I had another client whom I told, “You know you could figure this out on your own”. She replied, “I have two businesses and three kids. I pay you to figure it out for me”.
I think both are correct.