The only reasoning I can see you'd stamp that on a gun is if it's a magnum semi-auto and shorter shells won't guarantee reliable cycling....but there are *no* Remington shotguns, or any other shotgun I can think of for that matter, that is designed for 3" and 3 1/2" shells and somehow becomes dangerous if loaded with a shorter shell. Most Remingtons won't reliably cycle Aguila shorties, either, but they are perfectly safe to fire in *all* Remingtons (and all other shotguns proofed for smokeless powder) if hand loaded.
But, as you said, that's beside the point.
If your shotgun is marked 3", it can chamber and fire *all* factory-loaded shells of that gauge up to that length.
rich