You are kind of right.
In a bolt gun with factory ammo, you will never see the difference.
In an AR, if you load to max for a 5.56 chamber you will need to back off about a grain in a true .223 chamber, or you will be picking primers out of your trigger group.
So if we're only talking about < 5% difference in maximum charge with a 5.56 versus .223 chamber ... It seems to me that you easily could find that much difference in any two rifles with the same NOMINAL chambering, correct?
In new firearms? I've seen that level of variance in other calibers, especially if we are talking modern firearms vs. worn old military chambers, but that's not what I'm talking about. In the .270, which I've shot a lot I have yet to see one in good working order where I needed back my max loads off 3 whole grains due to a tight sammi spec chamber.
Modern low round count barrels in good working order. Sure you will have some differences, but in my experience, if you don't back your max 5.56 loads off a grain for a .223 chamber you will not like the results.