OTOH, you might expect the corporate media to also come from broadly different perspectives. Yet the corporate media output is strangely uniform in their bias, narrative and messaging ("The walls are closing in!... this marks the beginning of the end!") The appearance of Fox news made this blatently obvious, and was an utter shock to the left to see how deep the chasm was between typical right wing thinking and their own thinking. The fact that corporate media is so uniform in their viewpoint (other than fox) raises the hackles of skeptical folk like myself, and has for me been impossible to ignore since the mid 1980s. I'm not calling it a conspiracy, I'm calling it uniform enough that you shouldn't consider a story more likely true just because you heard it from multiple corporate media sources. For one: they cheat off of each other.
You don't have to look far to see how the news media is co-opted by political agenda. NYT Dean Baquet was caught on tape instructing his journalism team that for the next period, stories were all to be about racism and how Trump is responsible for racism. Slate broke that story. The next day I can't remember the exact headline but I think it was on budget cuts or something and they managed to blame it on Racism and the racism they blamed on Trump. It was laugh out loud funny -- how could budget cuts be due to racism? It was very sad.
On any given day, in any newspaper, I can point out the manipulative nation-damaging bias clear as day.
ObExample: Today, New York Times: "How a Divided Left is Losing the Battle on Abortion." This story fails to mention the most important context, context that they have repeatedly failed to mention for so long that most people are unaware of it: Abortion is not a federal issue. The 10th amendment explicitly lays out what the Federal government is allowed to do. The 1973 Roe vs Wade decision was atrocious in that it utterly overstepped the federal government's constitutional bounds. That decision is a null and void opinion of an institution that has no jurisdiction over the matter. Regardless of what you feel about abortion law (personally I think us men should leave it up to the women, but if pressed I'd be happy with a 20 week cutoff), the collapse of the fundemental underpinnings of the United States is a much bigger story, rarely if ever mentioned by corporate media. Instead they evoke images of coat hangers to get you all emotional, frame it as a human "reproductive" right to make you indignant, and use other framing tactics which speak to and draw people into the left's vision.
CLARIFICATION: I randomly picked a story. I can do that with any story, because they are all like that.
No, they haven't. If you pay attention to any mainstream media source you'll see that they all eagerly (sometimes to their detriment) incorporate web and social media content into their coverage, and maintain active presence on multiple social media platforms. It's a myth that "big media" is terrified of the web - far from it. They see the web as a cheap and easy way to farm content and cut costs. There hasn't been a meaningful distinction between "old" and "new" media for years now.
The only story similar to the one you describe that's being pushed is that the all mainstream news sources are dangerous, untrustworthy and fake, entirely co-opted by corporate interests and a political agenda, and that only the web can be trusted... when the web is even more deeply co-opted by those elements than the mainstream media.