It's a good thing I happened to read this thread. I consulted with a Parker expert I know and he told me the late Parkers only say 'Parker' because Remington did not have enough money to buy the Bros part of the name. So they settled for just Parker - kinda like when you want cheese on your hamburger but can't afford the extra 50 cents. It is entirely possible that someone ordered the gun in the late 1930's after the Remington takeover and they were just using up the remaining supply of parts which, according to some records he had, included laminated barrels and enough odd parts to make a hammer gun. The laminated barrels were probably made by Parker, not imported, and may shoot better than barrels made of other types of steel.

I'm glad this mystery has been solved. If you ever need solid proof your gun is authentic, just stand a little straighter and tell the fool who would question you, "Remember, when it comes to Parker, never say never!"