I am not a personal trainer, but I work at an athletic club as a dance instructor, and some of my co-workers are trainers.
From my personal experience, I think sometimes it is *good* to touch a student/client. Sometimes in class, I can say out loud for someone to move their feet or move something to correct their form-but sometimes they don't "get the feel of it" until I move them physically. It is usually something very slight-such as pressing down their shoulders, adjusting an arm position, etc.
It isn't ever anything creepy or touchy-feely, but when you are exercising or dancing, proper form is important-and when it is done, it is done so to ensure that you get the results that you want, and so that the activity is safe for you.
How much touch is involved depends on personally. Some students I have never had to touch at all (they naturally have great form, or correct it when I verbalize it) and others I have to correct more often.
I understand that you have a thing with personal space, and I do as well in everyday situations, but when I go to a dance intensive myself-I want to be corrected/moved if I need it. The reason that you are paying for someone to train you (in exercise or dance or a sport...) is to be coached and taught to do it correctly. You don't want to pay, and have them let you do it wrong. So, just think of it as being corrected/guided, rather than someone touching you for the heck of it.