It's a great point, and well articulated. In the case of the example in the post (fraud), the credit card industry has actually termed the false positive rate

It's a great point, and well articulated. In the case of the example in the post (fraud), the credit card industry has actually termed the false positive rate the "insult rate" (because the customer feels insulted in the store that their charge has been declined), which certainly gives you an idea of how they feel about false positives.