It is very true that you don't know the back story, although since the same thing was going on with every student it doesn't sound like there was a lot of great teaching going on. But you never know.
I have one student who I've had for years, who simply doesn't pay attention to her basic skating technique until I've spent 10 minutes giving the same corrections I've been giving her for, literally, years. So I've begun starting her lesson with very simple drills--forward swing rolls, backward swing rolls, etc. If she skates the first round making the same mistakes, being sloppy simply because she's not bothering to focus, I now simply tell her, "do it again, and fix it." She knows perfectly well how to do it correctly. So bent free legs, sloppy feet, looking down, no power---those do not get immediate corrections from me, unless she's done the same thing a few times, and then, yes, I'm pretty short with my correction. I'm trying to get her to be aware of her own body lines and be responsible for skating to a certain level without my having to waste lesson time every single week on stuff that she should be owning herself at this point. And it is working--she's much more pulled together right off the bat, because she's learned that she doesn't get to do anything but basics until she does it right.
That may sound a little harsh to an outside observer, but they wouldn't know the history.