That's absolutely correct. I workout with a trainer (I know how most people on this forum feel about trainers but, I know I don't know how to do things properly with the right form so I have a trainer and it works for me) and we start heavy (enough to where I have proper form) and as soon as my form goes south, I get stopped right then and there immediately and we lower the weight. We start with higher weight at first, then I start getting fatigue throughout the workout, and so we have to lower the weight to keep my form correct. Sometimes we even have to come down to an embarrassing weight but, I have to do the routines properly with the correct form, it's the most important thing according to my trainer.
I have no idea what hes doing where he's starting with lower weight and building up to higher weight. My trainer has me do the opposite because when you first start, your muscles aren't as fatigue you can do more reps, you can do more weight etc. but throughout the workout you start tearing your muscle fibers and you start getting fatigue so you are able to do less it gets harder. You must not be tearing down your muscle fibers properly if you are actually getting heavier as you go a long. Just my guess, I'm no expert and always learning, anybody can feel free to correct me if I'm wrong.
Its called ramping the weight. You build up to the weight to get warmed up and get used to the load. Jumping straight into a max weight is dangerous as hell when you start hitting some big weights.