Sure - but that's true of every site on the web. Conflating mainstream media's reach with Twitter's is fairly disingenuous, since mainstream media also highlights basically every other platform in similar ways.
The brief exception to this is politics - where Twitter was an easy way to get a relevant soundbite from a politician on a topic. I think that era is waning very quickly.
Definitely not true of every site on the web. I tried searching for mentions of hackernews (a relatively large forum, and also vc backed, not independent) on the nytimes website. One result https://www.nytimes.com/2013/03/24/magazine/the-3-10-13-issu...
Most media sources aren't embedded in small forums.
Admittedly - it's fairly certain that some of those will be about ycombinator itself - but I don't really find that outside the scope of the ask - given that many of the hits for twitter are really just following the company drama and not expanding the reach of a single user's tweet.
Couldn’t find a single other mention of the specific website. I don’t think talking about the company counts, since we’re talking about how much things that circulate on Twitter make it in the news. I can point you to 1000s of tweets that have been in nytimes articles, but only 1 hackernews post
The brief exception to this is politics - where Twitter was an easy way to get a relevant soundbite from a politician on a topic. I think that era is waning very quickly.