My understanding is that these guys are becoming increasingly aggressive in their attempt to show how "the gun show loophole" is allowing crazy illegal immigrants who've committed felonies to buy guns. If someone offers to buy a gun from you, but won't show you (1) something that identifies who he is and (2) that he's a resident of the Commonwealth *; OR tells you something like he probably couldn't pass a background check; he's probably scamming you with the intention of having the VSP take you out in handcuffs.
If something like that happens, ask the prospective purchaser to wait a minute while you "go ask your friend, the real owner of the gun" if he's sure he wants to sell it, or some such excuse. Then go find a cop and report the felonious attempt to gain possession of the firearm illegally. The mere attempt to acquire the gun is a felony. And the cops CAN arrest for a felony not committed in their presence. So if they say, "that's a civil matter", or "I didn't see it happen", ask them whether they're personally in favor of felons acquiring weapons unlawfully at gun shows, because you think the news services would have a field day with that one. And be sure to look at their name tag and badge.
The NYPD are NOT law enforcement officers in Virginia! They are NOT cops while they're here, and they have no law enforcement authority. So if they attempt to purchase weapons knowing themselves to be residents of another state, that's a felony in Virginia!
(* The documents proving identity and residency don't have to be the same document, though a U.S. Passport or a Va. driver's license would do for both, if they state a Virginia address. And it is possible for a person to be a resident of more than one state for gun transfer purposes, so someone could show a S.C. driver's license that identifies them, along with a property tax receipt showing a residence in Virginia. It's lawful for such a person to purchase a firearm in Virginia during such time as he's actually a resident of Virginia, even if he lives somewhere else most of the year.)