Comment by kurthr
This is a really key result. You can't effectively be "blind" to a parameter that is significantly correlated to multiple inputs and your output prediction. By using those inputs to minimize false positives you are not statistically blind, and you can't correct the statistics while being blind.
My suspicion is that in many situations you could build a detector/estimator which was fairly close to being blind without a significant total increase in false positives, but how much is too much?
I'm actually more concerned that where I live even accuracy has ceased to be the point.