I hired a company to hang drywall on my ceiling and then finish all surfaces so I could paint. Included are pics I took of a few of their more excessively-sunken screws. I said to one of the guys, "Not to criticize your work, but aren't you driving the screw too deep?" He said, "The head of the screw can't be flush to the drywall surface. You have to countersink it like this so that you can mud over it."
I agree with that statement, but what I've learned is that you're supposed to dimple the screw in, not drive it through the paper. In these pics, it definitely looks like the heads broke the paper.
Does this require repair to be considered a sound installation?
This is type-x gypsum. I think that brown color you're seeing is from the fibers of the paper being pulled into the hole.