I doubt you'd measure success exclusively by the number of false positives but you'd also need to factor in the impact of a false positive.
For eg: There was an x-ray machine [1] with a software bug that would accidentally deliver a dose 100 times the intended dose. I'm sure the machine operated correctly thousands of times however there were "at least 6 accidents" and 3 deaths (worst case scenario). One would not say that this system works.
Millions of success events vs. 1 human error has no conclusions except that the system works.