As I wrote above, I think this rule is completely stupid, especially because Russian citizens allowed to make photos and even videos there and internet is filled with pictures from there. But the museum is the property of Russian military and as any military, and Russian one especially it's has a million idiotic rules. As Russian saying goes: "Who had served in the military doesn't laughs in a circus".
Actually Russian Caucasus regions have some type of border check points wich separates them from the rest of Russia.Most countries have some areas or places that foreigners can't go to though, or areas that you need security clearance to enter. I've come across it in several countries.
I read in a guide book that there are whole cities in Russia that foreigners can't normally go to. Several cities (not sure which ones) and also areas in the Caucasus and border areas. I wonder how they check to make sure that foreigners don't go to these places in the Caucasus.