Around the world? I think you are overestimating Twitter by a large margin. My guess is that in the US Twitter has marketing deals with media outlets which make it a relevant platform to post and consume breaking news in the first place.
In other countries I haven't seen a lot of Twitter logos on TV.
The GP means that the journalists at the TV stations are getting their leads on what to cover from Twitter; not that audiences are watching Twitter in place of breaking news.
They probably have a police scanner running too. Should the public have that running as well to listen to all the latest news? IMO there is place for that and most people don't really need up to the second information on things happening hundreds of miles from anywhere they regularly interact with.
Who said anything about the public? A "breaking news platform" being of relevance to journalists is valuable enough for it to be a large company; whether anyone from "the public" makes direct use of it, they still indirectly depend on its existence.
Nothing to do with TV, Twitter has been established as a news breaking platform since at least the Arab spring. And it is absolutely an international phenomenon.
TV has nothing to do with it. I've never seen a Twitter logo on TV in the US either, except when they're reporting on Twitter as a company. GP wasn't talking about a business relationship between TV networks and Twitter.
In other countries I haven't seen a lot of Twitter logos on TV.