They are at some level. Of course, a newspaper isn't going to present all sources as being of equal authority. If someone is spouting nonsense at some point you cut them off.
The media clearly has power. And it's not wrong to observe that the mainstream English language media tends to be associated with a certain class, worldview, and educational system.
On the other hand, there has never been an era when individuals had as much ability to male their voices heard or, for better or worse, such diversity of news (and "news") sources.
There's also the fact that Twitter is a platform and not a publication. And there are certainly questions of what happens when dominant platforms that control access to eyeballs start regulating what people can people can publish there according to reality as it exists for the tech world.
They are at some level. Of course, a newspaper isn't going to present all sources as being of equal authority. If someone is spouting nonsense at some point you cut them off.