As this is all third-hand at best and the individuals who were denied boarding are not on this thread, it will be hard to get to the bottom of it, but I have to wonder whether the issue is not whether the test was conducted by the NHS but whether the certification of the test result was, in the instance of that group, insufficient.
The requirements are made by the Dutch authorities and the burden of checking placed on BA/KL. But, BA/KL are not making social judgments.