Ammo for the 5.56 NATO originally was limited to the same pressures as SAAMI .223 Remington, but there was an allowed increase of about 3000 psi back in 1999 and I believe is was applicable to M855. Beware of loading data that gives the green light to 62000 psi. Here is how it was to be done in 1984.
I have a copy of a 1999 document which indicates the pressure limit was upped to 58700 psi average, but I cannot find a link to it.
M855A1 is said to be loaded hotter but I have found no specification documents on it and it may be that it is still classified. In addition to all the positive hoopla that I have read about the A1 round, it has also been said that the military is experiencing longevity problems with rifles firing the M855A1 round. I have not looked into the question for about eight months so there may be newer info out there.
Regardless, I am sure that many of us are loading what we intend to be .223 Remington ammo beyond the 55000 psi spec. We have no way of knowing.
If the intent is to load to 5.56 NATO spec, it would be foolish, IMO, to strive for 62000 psi. That 62000 number is lifted out of a European spec for 5.56 NATO ammunition that is developed and tested using an entirely different measurement method.