I think this just makes things even worse.
Real news cost $ to produce. If publishers charge for access to real news, then what we are left with by default is the fake "news" that is so cheap to produce that it can be ad supported (or serves some other end that makes it worthwhile).
A critical problem. The focus needs to be on providing 'real' news more than dealing with the fake stuff. Also consider:
1) Probably the vast majority of people online and who will be online, including in many poor countries, cannot afford a NY Times subscription. People who through the miracle of the Internet would now have access to objective, top-notch news coverage will now be shut out.
2) Parties who want to spread propaganda are the ones who would be willing to finance free publications.
3) Will the NY Times be part of the online conversation if only a small subset of the online population can read it?
I don't know a better way for them to fund themselves, but it's a serious blow to the public and their knowledge of the world.
Just a brainstorm, but perhaps this is a problem Facebook as the power to address? They want to get into providing content, and they have the resources.
And not to toot my own horn here, but I work for a mid-sized library (metro of about 200,000) and we subscribe to every regional newspaper. If someone wants to be better informed, the resources exist.
Since you decided to toot, you open yourself to questions: Can local citizens read those newspapers online? Traveling to a building and reading yesterday's news on paper is not realistic and at this point it's an anachronism.
But to answer your direct question, no, they cannot. Our local paper is fairly stubborn about its monitization (refusing to digitize back issues in major library databases such as Proquest), so I'm not optimistic.