Beware, you are making a strong assumption: that the test's accuracy is the same regarding false negatives and false positives. For example, a test may not find enough "anomaly" in an ill person to trigger the positive, thus yielding a false negative; at the same time, it may as well never find any "anomaly" in a sane person, and as a consequence never give any false positive.
Back to your example, it's obvious that a test with a 0.01 probability to give a false positive is completely useless for an illness that affects 1e-6 of people.
Actual descriptions of medical tests routinely give both rates. They often call them "sensitivity" and "specificity". Good luck remembering which is which.
But if only one rate is given, that indicates they're equal. If they're not, then it's reasonable to describe the documentation as incorrect.
