Media coverage might blow their cover. If business people perceive a market, then they will enter into competition and lower profit margins.
"if some business really wants to remain private about their success, then why blame the media or anyone else for not talking about them"
Because it's the news media's job to tell us about interesting and important things that are happening in the world, regardless of whether the people directly involved want us to know. If you get your facts from the news, you get a distorted picture of how money is being made, and that means that the news has failed you.
Little what i understand about publicity, if you have a reasonable story (of an online success) and are willing to push it, you have a fair chance of getting it covered a fair bit. Obviously, to reach Google & Facebook news levels, you have to become as big as them.
p.s. This could be an opportunity for some 'website' (not a startup) to cover successful online businesses and their stories. Or may be there already is a one ..