There have been a variety of threads on this over the years, which you can probably find by searching the forum.
I wish I could remember who it was to link to the post, but some years ago, a user posted a link to a scientific paper written by his own orthodontist, in which it basically said along the lines of "the patient wouldn't wear it so I made it so he couldn't".
I've long held the view that there probably were some orthodontists out there who, once upon a time, and probably with the authority of the patient's parents, made headgear non-removable in one way or another. It has also long been my view that it probably hasn't been done in 30+ years, not only because of the general decline in usage of headgear.
As the saying goes, "truth is stranger than fiction"!