I think I found another glitch in the game (or a loophole in the "rules").
I had just finished the Book Depository/Repository in the Milkman Conspiracy and was leaving the area. I had the gun in my hand and left the sniper area and immediately jumped down the manhole to transport back to the previous neighborhood.
I wasn't holding the plunger, I was holding the gun. The sirens should have gone off and I should have been interrogated but that didn't happen. Instead, I just popped out the other end.
Maybe the spies have to be present when when you enter a secure area without the proper prop in order for the interrogation scenario to happen.