I also wasn't allowed to smoke pot, while enlisted.

Which is to say, the orders may not be followed by the persons at the switch. I make no claim that they will, or will not, be followed. I merely point out that rules aren't always followed.

Correction: Overriding POTUS is illegal and has consequences that do not include the planet being nuked.

They absolutely have the real authority (ability) to refuse the order, and then the real authority to prevent the nuke from being launched (by eating their key, shooting anybody else that comes into the room, shooting the key/console, etc).

Though as I understand it each missile site has its own control and 2 man system. Even if only 1 out of 10 obeyed their orders and launched it would likely be the end of mankind or at least civilization as we recognize it.