Not true, at least in the US and Russia. More than one person in the chain of command needs to commit to an all-out nuclear attack. It is perfectly plausible that someone along the chain would not follow such order.
Here's a twitter thread (in German) explaining how this supposedly works in Russia: https://twitter.com/SwenRoschlau/status/1498575623941505026
If the method for delivering the nuclear order is routine and 99.99% benign (except for the 0.01% where it's not) and the order is checked only by machines, then no one would know except for the person that made it.
Further, to enforce compliance with routine behavior, one just needs to threaten the family of the subordinates. Or better yet, occasionally take one of your subordinates and make an example out of them, once every two years say. Send them and their family to labor camps never to be seen again.
The only way to disarm the world of nukes is to unite under a rational, evidence and incentives based, benevolent world government. There's literally no other way to get rid of nukes if you've studied it.
Even if every nation disarms they all live under the threat of another building them in secret. As soon as one of them suspects as much the race is back on to re-arm.