What military would use will have a 'mil-std' number labeled on boxes and not likely the colorful eye catchers you see on the ammo shelves.
For years, I bought military surplus small arms propellant for reloading, came in 10 pound drab olive green cans stating contents. Had burn specifications on the can and a manufacturer number, no names. Best, most consistent powder I ever came across.
You find mil-spec ammo, it will probably be in large bulk shipped in wood crates.
As for Wichester, never heard of bad ammo and have elevated quality control on their high end ammo,especially the hunting stuff.
I use their primers, and a hundred thousand, never had a bad one.