From military officers I've talked to, there's more involved. Even if the POTUS advisors (people at the white house) can't stop the order, if something totally whacked out like attacking Italy was ordered, there are personnel literally in direct control of the weapon systems who have a hypothetical opportunity to intervene.
I feel we have discussed this before. Perhaps it was LVWood and/or Chemsoldier who commented. Either way, I don't think Trump could do a few lines of cocaine, get in a fight with his wife and order Melania's native Solvenia to be nuked.
While the process and protocols may be expedited, I believe there are controls in place for certain contingencies.