As @CeciledeVolangesdeNouveau alludes, this is all to do with Signal Detection Theory, which I actually understand (and some statistics, which I am not so strong on
). Any detection system will throw up false positives, but of course no-one knows at the time that they are false positives, they just know they are positives.
So they do what they should do when they get a positive - mitigate the risk, by moving people to somewhere with a different water supply, in this case. Can't have your customers dying of a water-born disease!
Of course, you can and should re-test, as the likelihood of two false positives in two tests is low (and can probably be calculated using statistical theory). And you never know, maybe in this case the source has been treated since the first test?
The other error you can get is technically called a Miss. That's the one to worry about in this case, because that would be Legionnaires being present, but NOT detected.
You can't eliminate these errors.
There's a bit more to it than this, but I'd have to go and look it up. There is no way of getting out of this problem - there is no certainty, only statistical probability.
.I must say, I am very disappointed that I won't be seeing Linney in a hotel room.