Not attempting to answer for TSA here, but my suspicion is that there are no privacy-friendly ways to resolve alarms.

The lawyers and the public probably won't tolerate body cavity searches (rightly so) of 85-year-old women, 3-year-old children, and in general innocent US citizens who happen to have used the wrong kind of lotion that day. And from a risk-avoidance and CYA standpoint, it's better to not detect the explosive than to detect it with an ETD and fail to stop it.