OK, they quote a lot of SAAMI stuff, which does NOT address firing 5.56 Nato in .223 AR15's. It is mostly about not using 5.56 NATO in OTHER .223 rifles.
I am not convinced. And THOUSANDS of people have fired 5.56 ammo in their .223 rifles without problems. In fact, I don't know of anyone having a problem.
Most of what IS discussed is that MATCH CHAMBERS are tighter, but this is not necessarily headspace per se. Semis have looser chambers to allow good functioning with full length resized brass. This is just the opposite of a match shooter with his bolt gun, who will neck size only. Yes, try neck sizing only and I guarantee you will not have smooth funcionting in your AR15.