It's not black and white though, you can have a regulated press that is still a free press, just like you can have a regulated marketplace. In fact regulated marketplaces work better, just as the press would if there was proper oversight.
If by 'regulated' you mean 'pre-approval of articles', that's censorship.
Anything post-facto is just closing the door after the horse has bolted, and I don't think fines are going to dissuade the owners of the right wing tabs.
It's not black and white though, you can have a regulated press that is still a free press, just like you can have a regulated marketplace. In fact regulated marketplaces work better, just as the press would if there was proper oversight.