I'm not really a gun guy, but according to wikipedia the 5.56×45mm NATO was developed by Belgium and, as far as I can tell, can be manufactured a lot of places not named 'Russia'.
The cartridge exist because of NATO.
I found a reference that Russia exports arms to 60 countries which came with a mention that 88% of Russian exports went to Asia, Oceania, Africa, and the Middle East. I was able to track down a list of the top 30. None of them are NATO countries and a couple were in South America or non-NATO eastern European countries. Some of them imported Russian equipment prior to joining NATO, but I couldn't find a single country that imported Russian military equipment after joining.
This really isn't a coincidence of course Russian stuff is going to be less sensitive to neglect and it's going to be cheaper. If you've been using Soviet stuff for the past 60 years there's not much of a reason to change, blame the Cold War Russians would send stuff to anybody that said the right things fuck even America would send equipment. Russian equipment made by the Chinese ain't capitalism grand.
Do you have a source showing NATO countries importing military equipment from Russia?