> 2. Two people who are identical except for their nationality face the same probability of a false positive.
That seems to fall afoul of the Base Rate Fallacy. Eg, consider 2 groups of 10,000 people and testing on A vs B. First group has 9,999 A and 1 B, second has 1 A and 9,999 B. Unless you make your test blatantly ineffective, you're going to have different false positive rates -- irrespectiveof the test's performance.
That seems to fall afoul of the Base Rate Fallacy. Eg, consider 2 groups of 10,000 people and testing on A vs B. First group has 9,999 A and 1 B, second has 1 A and 9,999 B. Unless you make your test blatantly ineffective, you're going to have different false positive rates -- irrespectiveof the test's performance.