I've used a Softcomm ANR headset for a few years that squealed when some people put it on. My guess was that it was an improper seal that let unwanted noise in causing a feedback, it happened particularly with people with a relatively small head size.
In the end though the explanations given above go to the root of the problem: cheaply designed electronics. I've had a lot of fun with the headset mentioned above but I could tell that it wasn't all that good (with ANR on there was a persistent hiss but the overall sound quality was pretty good, and with ANR off it reverted to a cheap headset with lousy sound quality). It did what it said on the box but I've now switched to a David Clark with ANR and that's a lot better.