That would decrease the amount of people correctly identified. And you're also under the assumption that the misclassification of people is a random phenomenon. In the real world that wouldn't be the case and some type of blood may get misclassified all the time by the system.
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It's probably not as simple as I think it is but if the test is cheap enough couldn't they just run it again on all affected people just in case?
If ran twice we'd have: 49 correctly detected, missing 11 cases and 250 incorrectly suspected.
Ran thrice keeping the 2 most similar results we'd have: Most people correctly identified?
That would decrease the amount of people correctly identified. And you're also under the assumption that the misclassification of people is a random phenomenon. In the real world that wouldn't be the case and some type of blood may get misclassified all the time by the system.