First, let me start off by saying that I agree with what I believe your actual premise is (or should be) - that articles in science journals should not be behind paywalls. I’m strictly against the practice, I think it’s a massive scam, and so does everyone I know who does research. I have paid to open source every paper I’ve published. Well, not me personally. But thank you taxpayers for funding me to not only do my work but to make sure you have access to it too. I’ll talk about this more at the end.

With that out of the way, I’d like to mention a couple of things. First, the scam is on the part of the academic journals, not the researchers or the journalists writing the articles. It’s not part of some scam to hide the fact that the journalist is making crap up. If the authors were unwilling or unable to pay the fees for open sourcing their papers ($3-5k when I was doing it several years ago), then you’re either going to be in an institution that has a subscription to the journal or you’re going to have to find some way of acquiring it.

Search for the exact title in quotes. Sometimes the Google Scholar engine will return with the default link to the pay walled page, sometimes it’ll have a link to a prepublication server. Arxiv is one of the more popular ones for physics, math, and computer science of all stripes. Step 2 is to go to the institution web page of the first author. Very often, researchers will keep an updated list of their publications with links to the PDFs. If that still doesn’t work, you can write the author and request the paper. We love those emails. We love it when people read our work, especially when they’re so excited that they wrote to request a copy. None of these involve copyright infringement. That prepub that you get is the same paper (usually but you can confirm with the author if that’s a question), but possibly without the masthead and layout from the journal. It’s still cited the same.

So, why are so many journals behind a paywall? Because the publishers want to monetize what today should be a cost free (or minimal) set of transactions. Here’s what happens:

1. I have an idea for some research. If it’s good and I’m lucky, I get money from the government (or whomever) to do the work, and I use it to pay my expenses (salaries, materials, equipment, whatever). I also get taxed on it by my institution so they can pay the admins and other costs. When submitting a proposal, those are all line items in your budget. If you’re doing expensive research at an expensive institution, it’s pretty trivial to set aside $10-20k for pub fees. If your entire grant was $35k, that’s a lot harder to justify.
2. You write the paper after doing the work. You don’t get paid to write the paper specifically - it’s part of the research that you are doing. The point here is that, unlike book authors, researchers see zero of any money you’d pay for the article. If you do locate a copyrighted copy, you’re not taking a dime out of my pocket. Again, just thrilled someone’s reading the damn thing.
3. You pick a journal and send it in. The journal has a contact list of researchers and their fields, and sends out requests for reviewers. They usually require 2 or 3.
4. The reviewers read the paper making notes on questions they have and recommend revisions before publication. Reviewing is an unpaid service researchers do because we know that’s how it works. The irony is that it challenges the academic notion of the tragedy of the commons. You could be a freeloader and never review, but enough people do it that the system keeps rolling.
5. You revise, reviewers approve, publisher accepts and schedules date. There can be some back and forth here (this is a legitimate publisher expense, but the level of effort and interaction isn’t like with a book editor).
6. Your paper comes out.

As you can see, the role of the publisher is very small in the overall amount of effort put into getting an idea from my head into yours. At one point publishers had an argument that the small circulation numbers for things like The Journal of Theoretical Biology justified their $21k/year institutional subscription price.

And I shouldn’t have saved this til the end, but for the one person who skimmed down to see where all of this was going:

Any science article / press release that cites a paper whether or not you have access to it at least is citing something that has undergone peer review. Peer review can only do so much and journal quality has a wide range, but it’s about the best we have. If it’s a big enough deal to actually matter and the media in question has wide enough reach to care, then it will get back to the author who can then clarify.

To add onto that, whenever a newspaper says "based on the findings of researchers at [Random University]" but they don't list the citation anywhere at all. That is just evil, but somehow industry standard.

I've had a field day while writing my thesis recently, realising I could bypass the paywalls by accessing the papers through the university proxy. It's still bs, though, because it leaves this stuff only accessible to researchers and not your regular people who may be interested.

Though like PrinceWith999Enemies said, many paper writers will happily send you a copy if you email them about it.

Unfortunately, most scientific papers are behind paywalls, especially the most prestigious journals. So this doesn't make much sense.