This image from The Post provides some extra background on the story. I'm guessing the reason that De Niro and Keitel are listed as also having a "premise" permit is that they have more than one firearm and aren't allowed to carry that other firearm for personal protection.
When I had my "target" permit while living in upstate New York I had to list the serial number of every handgun on the license. Those were the only firearms I was legally permitted to handle. So if a pal of mine and I owned identical guns it would technically be against the law for use to shoot the other's pistol, just because the serial numbers were different. Smart, eh?
I pushed our local cops on this issue and asked if it was against the law for my wife to use my gun in the event that an intruder came into the house while she was home alone. They hemmed and hawed and I never got a straight answer because, I suspect anyway, that by the strict letter of the law she wasn't allowed to touch it.Again, brilliant.
But this goes hand in hand with the attitude that a barrel shroud or a pistol grip is what makes a gun an evil object that should be prohibited.