So, if I get an "Alarm Resolution Pat Down" (as the fark user called it), it appears that the following applies:

1. SATTSO is correct - a TSO is not performing it
2. SATTSO is also, quite deliberately IMO, obfuscating the issue, as an LTSO or STSO is (key takeaway - to the public, a uniformed member of the TSA is a TSO, regardless of the amount of stripes on the epaulet)
3. The passenger is forced to permit this resolution procedure in a private room; sounds like a detention procedure to me, which would take us out of the realm of an administrative search, based on my recollection of the recent court cases against TSA