Its also a reflection that the fault protection needs to leave the circuit undamaged, whereas it does not matter if the fusewire is glowing red hot for a brief moment (it has no insulation to burn off!).
So that means limiting the terminal temperature of the conductors so something that won't destroy the insulation - so for "normal" sized PVC insulated copper cables that is 160 deg C.
That level of protection is in effect part of the k factor used in the adiabatic check. So if the sum says you have enough copper CSA, then its telling you that the worst case final temperature after the fault is cleared should still leave the insulation undamaged.