From what was described in the NYT article, the tests are not “unsound”. Nor are those making the tests inherently corrupt or malicious (some medical testing companies are, e.g. Theranos, but the same could be said of any other occupation or industry). My impression is that people who design these tests go into the field to help give parents the best possible information, and do their best to make tests which are as accurate as possible. (Disclaimer: I don’t know anyone in medical technology, pharmaceutical, etc. industries.)

The tests are extremely good, but they are not perfect, with a specificity in the 99.9%–99.99% range, which is low enough that there are more false positives than true positives for extremely rare conditions. Making tests with specificity in the 99.999% range or beyond is an inherently extremely hard problem.

The current quality would be fine if the posterior probabilities were properly explained to patients and if physicians had enough basic intro-level statistics background to interpret the test results. Unfortunately patients often aren’t given the results directly or told accurately how to interpret them and apparently many physicians lack basic statistical competence. It isn’t too promising that this NYT article expressly aimed at clearing up laypeople’s misconceptions does such a poor job explaining the subject, and spends its first half on misleading clickbait about how “wrong” the tests are.