Really depends on which leaders are said to have done wrong.
Your title also implies you'll discuss false news in any respect but I didn't really pick up on that. Part of the reason America (and quite frankly the rest of the world) have become desensitized to the news especially recently is that, for those who actually care about what is real and what isn't, it's becoming clearer and clearer that the media is heavily skewed to one side.
Part of your reasoning for why viewers don't care is, for the side that thinks the news is right, they look at the news showcasing heavy racism and other "hate crimes" and go "I knew it", then turn away. For the people who don't agree, they look at the news and say "Well, that's probably bullshit", and again change the channel.
So it's less an issue w/ the people and more the media outlets themselves are corrupting ability for people to find the truth.
RE: Fake/real news and the American Fool