There was always a difficulty about getting court decisions. Up until about 120 years ago, in both England and the US, court decisions were available as books, published almost invariably by private printing houses who sometimes had a contract with the govt for this purpose, and usually had some sort of exclusivity agreement - that they were the only people who could print the collected court decisions. This last part was almost a necessity because there was virtually no way to recoup the very considerable expenses of publishing the court decisions if two publishers were competing. The drawback is that, as different publishers handled decisions from different eras or from different courts, the multitude of different court reports - with some old ones unobtainable and the quality and features varying from edition to edition - made for confusion and errors.
In England about 130 years ago one publishing house undertook to reprint virtually all the known court reports published before 1865; this was the English Reports - Full Reprint, and it is 170 thick volumes, reprinting 274 court reporters going back to 1323 and ending around 1865. Making the ancient and rare reports available again, and printing all those decisions (about 100,000 decisions - some in Latin or Norman French) in one place - and with uniform editorial features - was a great benefit to legal research.
Shortly thereafter, the West Brothers in Minnesota undertook a similar project, to reprint in a small number of regional reports the decisions of the principal state and federal courts. They started around 1880, and by the year 1910 had gotten so good at it that they introduced that key number digest system. By the end of its career as an independent publisher, circa 1990, West Publishing was probably the biggest publisher in the entire world, printing virtually every published state and federal court decision and editing and annotating codes of the federal govt and about 40 states. Around 1880 also, Lawyers Cooperative Publishing Company, in Rochester NY, undertook to reprint all of the US Supreme Court decisions (previously scattered among more than a dozen privately printed reports) in one complete and continuing set, with such editorial blandishments as summaries of the briefs submitted in each case. So effective was Lawyers Co-op in doing this, that Lawyers Co-op unearthed and published about fifty decisions of the US Supreme Court which had gone unprinted over the years (the Supreme Court itself, prodded by Lawyer Co-op's discoveries, printed those neglected decisions in a bundle in volume 131 of the official US Reports. And so on.
Before the big buy-outs and mergers of the 1990s, West had virtually cornered the market on court decisions -- if a decision didn't appear in a West reporter - even though it might appear in any of a hundred other legal publications - it was commonly regarded as poor precedent and a lawyer would have to justify going outside the realm of West to cite such a decision.
When Thompson started buying up all the legal publishers - including both West and Lawyers Co-op - the US Dept of Justice began an antitrust action, which is how Reed-Elzevir got into the legal publishing business, having bought whatever publications Thompson was forced to divest (which did NOT fall along the same dividing lines that had existed between publishers before Thompson bought everything up).
There was also, about five years ago, some very aggressive litigation between WestLaw and Lexis over their legal databases and what each could offer; it ended with a settlement that allows both of them to carry pretty much the same statutes and court decisions (albeit with different blandishments regarding explanatory materials).
I use both Lexis and WestLaw in my work. They match each other in reprinting about 100% of the decisions published in regular court reports. They have an overlap of maybe 90% on unpublished court decisions -- it's usually the judges themselves who decide that a decision shouldn't be printed in a hardcover volume but that decision might still be available via "electronic reporting"; the 10% unique to each is what's interesting.
But WestLaw and Lexis have little discretion about choosing to publish decisions. It is the courts that transmit the text of their decisions to both West (including WestLaw) and Lexis; the judges decide which decisions will be printed in book form and which are only to be available in "electronic format" - and the service that doesn't comply might get disconnected from future court decisions. At the same time, courts have their own websites usually offering (for free) their own text of their recent published decisions. Only a very tiny fraction of court decisions are destined for publication, not as a result of anything sinister but because most decisions say nothing new or interesting.
So the situation isn't quite as sinister as painted by this article.