I think the point being made is this. You shouldn't be sitting at the gym because you think your child might be abused. If you have even that little suspicion that something is wrong, you should be high-tailing it out of there, not watching to make sure. The fact is, MOST abuse happens in residences, by relatives or someone in the home. It is up to US as PARENTS to teach our children what is ok, what is not, and how and who to tell. It is up to US as PARENTS to have that relationship with our children that they CAN tell us. and, yes, it is up to US as PARENTS to remove our child from a situation that is abusive.
So the original point of "I stay to make sure my child isn't being abused" is the one that I see as eroneous. Not the thought that kids can be abused by coaches. We know that is true. But dunno's point about how that usually happens is spot on. Kids go home with coaches, kids are alone in the gym with coaches (no 2-deep leadership). If htose things are happening, then the red flag waves high.
But, from a viewing area, through a piece of glass, what are you going to see? Hear? My son gets chewed out at least 3 times a week for doign something boneheaded. But that is not abuse. He gets pushups, arm circles, or heaven-forbid, kicked out of gym, but that is not abuse. They are in a dangerous environment where even the slightest moment of inattention can cause serious injury. Some parents might see pushups and "yelling" as abuse. But a lot of times, they keep the kids safe.