In a semiauto, the 223Rem versus 5.56x45mm chambering issue becomes more problematic because reliability usually suffers if excess pressures are encountered.
The actual pressure level of a 5.56x45mm as opposed to the 223Rem isn't so much the problem(doesn't help) but the greater issue is how the bullet is seating into the rifling. Generally the 223Rem chambers are going to have a freebore in the throat area that is closer towards the bullet while the 5.56x45mm chambers allow for a little more freebore.
That's where some of the problems might arise, especially in semiautos, where a 223Rem chamber with a shorter throat causes a bit of a bump in chamber pressures if a round loaded to 5.56x45mm spec winds up putting the bullet too close to the lands of the rifling.
If it was a bolt action with typical Remington "mondo freebore" throat where a bullet can be seated out a surprisingly long distance before contacting the rifling, I wouldn't be too concerned if I used 5.56x45mm nato. Would be something I'd want to check out first, usually that's one of the first things I investigate on one of my firearms while developing a handload is to find correct seating depth.
The whole not using 5.56x45mm in a 223Rem chamber is a bit overblown in my opinion. Simply stated I recognize that some chambers will give a person fits if 5.56x45mm is used in a 223Rem chamber, in semiautos especially. But other 223Rem chambers out there have shown that it will reliably tolerate 5.56x45mm nato, my JP Enterprises accurized AR15 being one of the rifles I've run into that will run some kinds of 5.56x45mm reliably.
I've come to take it as the "your mileage may vary" sort of thing.