The NRA point is that guns not in active use should be verified unloaded.
"All guns are always loaded" is clearly not true - while they should always be approached with that assumption, they shouldn't BE loaded unless they NEED to be loaded.
OTOH, it's a mentality which demands respect for any gun, regardless of its believed condition of loadedness or unloadedness.
Suppose you were to ask whether my XX-XX (rifle) is, right this instant, loaded or not. Fact of the matter is, I DON'T KNOW. It's probably locked in the safe (that's what I remember last doing with it) and its chamber is probably clear (I remember doing that before I locked the safe). If I need to use it, I will be sure to grab some appropriate ammo along with the rifle itself. BUT, when I open the safe and take it out, I will "assume" that it is loaded and check to be sure.
Because all guns are always loaded.
It's not just a rule, it's a way of life.