And a large part of social psychology concerns the way in which we present ourselves to other people so as to make the maximally positive impression even when that impression isn't true.
If the true-positive rate is significantly less than 100%, as it would be for cheaper tests, then the posterior probability could be only 1% or even less.
By sending an email that repels all but the most gullible the scammer gets the most promising marks to self-select, and tilts the true to false positive ratio in his favor.