Not sure what the NCARs say, but there are pilots at W3 that fly the HS125 and B737 concurrently. I saw that one of the guys you're referring to recently got upgraded to the LHS of the Sovereign, but I'm not sure how that affects his B737 job.
Even worse still, the guys in the last hangar (another government agency) use first officers that aren't type rated on the aircraft. They're supposed to sit in the RHS and handle the radios