I don't watch these shows but these kinds of outbursts were inevitable by bringing in people like Britney Spears and (especially) Demi Lovato on as judges ... While I'm not as negative about singers like these as some people are, these girls are famous for reasons other than their singing ability; and are not well respected enough to give harsh criticism.
Most people with a good ear and a decent musical background can probably judge the singing ability of the people on shows like this, but to let people down in a harsh way you really have to have the person's respect. To use an analogy that is appropriate for this site, if you made an indie game and someone like Shigeru Miyamoto lists off a dozen things he thinks are critical flaws with your game you will likely take it better than if it is the designer at Ubisoft who makes all their petz games; even if they said exactly the same thing.