Is that the right characterization? If everyone got a test every year, then there would be 3% false positives, per the article.
Brain cancer cases are around 6-7 per 100,000 per year.
So that means simply screening everyone would produce around 99.8% false positives, wouldn't it?
Or, looking at it another way, there would be 400 - 500 false positives for every real one.
"More data" implies that you use it for something. If there is some kind of intervention, and it almost always is not needed, then it has to be that much safer, in order to not make people worse off in aggregate.
This has long been a controversy with mammograms, I think.