I found this thread because I'm reading Doctorow's "Little Brother", which by the way contains a few paragraphs about false positives, same as this article. I think you're splitting hairs to say it's not a correct statement. It seems obvious to me that there was an implied "of the times the test detected an infection" in there. That's his entire point - a 99% accurate test, for a one-in-a-million event, will tell you that event occurred 10,000 times, and be wrong 9,999 times.
I agree that I might be splitting hairs. But I'm in research, and I guess it makes me sensitive to incorrect statistical language. When I think of the accuracy of a 'test', I am thinking about the degree to which I can trust any result the test gives. Doctorow was talking about the accuracy of one result that the test gives, and then painting the value of the test in that light. It's worth considering, but it should be remembered that all those correct negative results are potentially valuable too.