Well, as I mentioned, I don't watch the show, but can't pretty much anyone judge whether someone can sing a cover? A lot of it is pretty much objective, isn't it? First, and foremost, the judges have to be familiar with the kind of singing that's showcased on that kind of show, and, after that, it's anyone's opinion. They are, after all, trying to find "talent" that a major hunk of Americans are going to like and be willing to dole out money for.
You don't get to be as famous as Howard Stern without knowing how to market to middle America (whether it's to win them over or piss them off).