IMO you are right re: investigation of PDSG as a prelude to a contract of such a sensitive nature. The PDSG organization along with any folks involved in any work on such a project would have to obtain appropriate security clearance via DISCO (yup DISCO, the Defense Investigative Service for Contractor Organizations). They enlist the FBI for personnel background checks and affiliations, etc., and do facilities security measures assessment. Such checks can be quite extensive, and time consuming (six months minimum is my experience, just for SECRET). I suspect that some/all of PDSG has already had at least some level of review prior to getting in the GSA catalog, since it's fairly obvious that this would be classified work/use. And I suspect PDSG has folks that are intimately familiar with DoD Directive 5220.20-M (Industry Security Manual).
FWIW,
SGE