Almost a quarter of a century ago, SAAMI recognized potential problems with shooters assuming that the 5.56mm cartridge was identical to the commercially available .223 Remington round. Here is their 31 January 1979 release, with some minor errors corrected:
With the appearance of full metal jacket military 5.56 ammunition on the commercial Market, it has come to the attention of the Sporting Arms and Ammunition Manufacturers' Institute (SAAMI) that the use of military 5.56mm ammunition in sporting rifles chambered for Caliber .223 Remington cartridges can lead to higher-than-normal chamber pressures and possible hazards for the firearm, its user and bystanders.
Tests have confirmed that chamber pressures in a sporting rifle may be significantly higher in the same gun when using military 5.56mm ammunition rather than commercially loaded Caliber .223 Remington cartridges, according to SAAMI.
SAAMI points out that chambers for military rifles have a different throat configuration than chambers for sporting firearms which, together with the full metal jacket of the military projectile, may account for the higher pressures which result when military ammunition is fired in a sporting chamber.
SAAMI recommends that a firearm be fired only with the cartridge for which it is specifically chambered by the manufacturer.
Additionally, SAAMI's Unsafe Arms and Ammunition Combinations Technical Data Sheet page states:
The .223 Remington is rated for a maximum of 50,000 CUP while the 5.56mm is rated for 60,000 CUP. That extra 10,000 CUP is likely sufficient to cause a failure in a chamber that's only rated for the "sporting" .223 Remington.