[Please be aware that I'm commenting on the reporting here not the ultimate result - starting at "Multiple discrepancies" section and the writing is far better looking simply at the evidence, indeed it makes you wonder how this wasn't pipped earlier, clearly no one compared the case studies to the paper???].
I'm surprised by the poor reporting in the start of the article, I expected careful balance and avoidance of sensationalism.
Three examples - reporting on the paper published in the Lancet 28 Feb 1998:
>“Onset of behavioural symptoms was associated by the parents with measles, mumps, and rubella vaccination in eight of the 12 children,” began the paper’s “findings.” Adopting these claims as fact,4 its “results” section added: “In these eight children the average interval from exposure to first behavioural symptoms was 6.3 days (range 1-14).”
I've not read the whole paper but there's nothing wrong with this is there? Adopting a claim that "parents associated [...]" as fact isn't wrong, or at least not provably by us. The association is apparently wrong but that doesn't speak to this result. The later result is not surprising as they would have been seeking incidences where there was a temporal association. I'm assuming that the paper didn't actually say there was an association (just a reported one) otherwise this article would have quoted that surely.
Two, the author questions how they would have had sight of the result before conducting the study. Fraud is possible, like Hubble's constant. But "knowing" the result is commonplace isn't it. One has a theory that one believes in enough to test, "this must be it, I think I'm really on to something".
Last is the questioning of the case histories, after talking to Mrs2:
>The next day, she complained to my editors. She said my methods “seemed more akin to the gutter press.” But I was perplexed by her story, since there was no case in the Lancet that matched her careful account.
Basically the author of the article is doing what has been so decried in comments here, they are trusting the (at least 5 year old) recollection of a layman vs the records of medical practitioners at the time. There is certainly more than one conclusion that fits including the possibility that Mrs2 gave a misreport to either the original study or Mr Deer. He also calls her account careful, but he describes her not remembering when the symptoms appeared being badgered into an answer.
Thankfully the article greatly improves as it goes on.
Parting shot:
>he and Barr explained in a confidential grant application to the UK government’s Legal Aid Board
Confidentiality isn't what it used to be!