This is nonsense, you have some pretty solid separation between the fiberglass (drywall, plywood etc) and there's no air movement bothering that fiberglass.
The separation is not as solid as you might think. In crawl spaces and attics the fiberglass is often exposed. And you can get air movement through these spaces, especially on windy days. My point is that fiberglass is all around us: houses, sports equipment, cars, etc. Just because something has fiberglass in it doesn't automatically make it hazardous. It may or not be, depending on the situation.
I used a gloves & mask when handling raw fiberglass for my tube traps, but I don't feel that is necessary when handling them now, or when being in the room, as they are fully covered with 2 layers of fabric. Do enough fibers escape to cause a health hazard? I doubt it, they've been there for 10 years and I haven't noticed any dust or fibers when handling them or when cleaning the room. Nobody has been coughing or sneezing. Since they're wrapped, I don't worry about it. Just my experience, anecdotes are not evidence, etc.
That said, I would not have an acoustic treatment with exposed fiberglass in my room. Even if the exposed fiberglass were inside, I'd want it covered to prevent migration of flakes/dust.
PS: let's not restrict this solely to acoustic treatments. I've seen speakers with fiberglass inside that are ported. Due to the driver motion you can feel the air pumping in and out of the port...