There are many manufacturers that mark their chambers as being 5.56X45 when they are actually not, so don't merely rely on the markings. I am not familiar with bolt guns and their markings, so don't ask; I am referring to the AR platforms. I was at a Dean Caputo class a few years ago and he used a chamber reamer from Ned Christiansen that showed just how far off/dishonest most of the manufacturers were as he cleaned out the chambers. Kind of scary. Colt/Bravo/FN/Daniel Defense/Larue/LMT/Noveske should be good to go.
In addition, you need to watch the milsurp in question to make sure it was not rejected as over-pressure. My recollection on the proper markings for that rejection is poor, but I am sure it can be found. Mix a tight chamber and over-pressure ammo and you might have a rough time of it. One of the first signs is popped primers falling into the guts of the rifle - if you get that, you have a problem and should stop until you know what it is and correct.