This is incorrect and is the source error that almost everyone makes - that Test False Positive+ Test True Positive=1
I agree with this, but in your example, the statement "the incidence of disease is 1% generally in the population" is not the same as "a patient referred for a diagnostic test has the chance of having the disease in question equivalent to the general incidence rate in the population".
If your contention in the example were true, then almost no one would ever believe a diagnosis of serious disease, because the chance of someone having, for example, Lyme disease as a percentage of the general population will always be lower than the chance of a false positive under that test.
However, if the person has been bitten by a tick and has certain symptoms, and the test comes back positive, the chances of that person having Lyme are really high. Because the chances of that person having Lyme prior to the test were way higher than the general average.
Your "fallacy" is dependent on the proper assumptions. It doesn't invalidate your point, which is obviously important, but it does qualify it.
Regards, TGW
“The trick is in what one emphasizes. We either make ourselves miserable, or we make ourselves happy. The amount of work is the same.” Carlos Castaneda