You're still also only considering false negatives (user is erroneously rejected). You have no data points about false positives (user is erroneously allowed).
If the sensor always detects and admits Bob, even when it's Alice, you'd have the exact same success data for Bob.
As far as I understood, the system is distinguishing between its members so we have some data about false positives because OP was always identified as themselves and never as another member.
Edit: this type of reasoning is probably what lead to the recent authentication bypass flaw in Intel's AMT code. It just accepts anything passed to it as a valid password hash. That test is probably still passing in their CI system...
This is 100% not the same type of reasoning. We have reason to believe that the fingerprint accurately distinguishes between 1000 different options. False positive and false negative aren't meaningful terms here, because we're no longer dealing with yes/no results.
"If this authentication system didn't work nobody would use it" is literally the reasoning I mentioned above.
> we're no longer dealing with yes/no results
That's exactly what we're dealing with. Iterate through the list of fingerprints in the database, does provided == stored.
You might be interested in reading about CER (crossover error rate). It's the term used for discussing the trade-off between type 1(false positive) and type 2 (false negative) in biometric systems especially.
https://security.stackexchange.com/questions/57589/determini...
I'm sorry, but you are simply fundamentally misunderstanding how this works.