You are right.

The military M16-spec chamber (commonly referred to as the 5.56 NATO chamber) is larger and has a longer throat to reduce chamber pressures with hot-loaded military ammo.  Commercial .223-spec ammo will work just fine in 5.56 chambers.

On the other hand, .223-spec chambers have shorter throats (being designed for bolt guns and for accuracy), and while firing hot military 5.56 ammo will probably not be dangerous, the increased pressure commonly leads to feeding and extraction problems.

-Troy