Not completely true. Everyone wanting to want to watch it at the same time causes issues. Other videos you can distribute the video to caches ahead of time, so the burden on the outgoing connection is less.
Edit: TPP had 60,000-70,000 simultaneous viewers on average, with a peak of 120,000.[1] In 2014, each NFL game had about 17.6 million viewers.[2] So an order of magnitude increase. How well does live streaming video scale horizontally?
[1]https://en.wikipedia.org/wiki/Twitch_Plays_Pok%C3%A9mon#View...
[2]http://tvbythenumbers.zap2it.com/2015/01/09/nfl-2014-tv-reca...
Granted that is 14 different events being streamed, but they eclipse Twitch in terms of live streaming by a huge amount.
[1] - http://techcrunch.com/2015/04/07/mlb-com-hits-home-run-with-...
Millions of people watching via livestream, overall (including TV), the largest annual TV event (197 million overall)
Livestreaming scales very nicely horizontally, if done properly.
And this is an event that is completely done without any ads or commercial investor backing it.