The SAAMI .223/5.56 interchangeability warning came out in 1979 just before the U.S. military came out with the higher pressure NATO SS109; U.S M855 round. Simple thumb rule, U.S. made M193 ammunition is loaded to the same pressure as .223 ammunition at 52,000 cup and was fired from M16 rifles with a short throat. NATO M855 ammunition is loaded to 55,000 cup and requires a longer throat the presently made M16/A4 rifles have.
I have two AR15 rifles and a Stevens 200 .223 bolt action rifle with a 26 heavy barrel, my Stevens 200 has a longer throat than my two AR15 rifles. (.0566 vs .0500)
The majority of short throated .223 rifles will have a 1 in 14 or 1 in 12 twist and the rest will have chambers and throats big enough to fit a firearms company lawyer in. (meaning they do not want lawsuits so the throats are longer on the majority of newer .223 rifles)
5.56 vs .223 – What You Know May Be Wrong
http://www.luckygunner.com/labs/5-56-vs-223/
HOLLIGER ON .223/5.56 CHAMBERS
http://www.radomski.us/njhp/cart_tech.htm
Military 5.56 Lake City cases are made of harder brass and are "NOT" thicker.
I have three five gallon buckets of U.S. military Lake City 5.56 brass, below is just one five gallon bucket being prepped for reloading.
NOTE: Some batches of Federal American Eagle 5.56 case have thin web areas and have loose primer pockets after the first firing.
To answer your question YES you can use 5.56 brass in your .223 and military brass is a higher grade of brass and designed to withstand higher pressures in larger military chambers.