I'm sorry if you don't believe it, but it really happens. The "coating" would have to be pretty thick, this gouge was something you could easily feel with your fingertip. I was very careful to not let my keys or anything else get near it, and the gouge (which was essentially the only scratch on the otherwise flawless screen) was exactly where my thumb hits the screen.

My Pixel 4a, meanwhile, was in my pocket all the time and never got a scratch.