In the USA, we don't really have "this person saved the world" stories, but we do have "these systems had mishaps" stories (there are many of these, ranging from "our wiring was wrong so when the guard thought he saw an intruder — it was actually a bear — it set off the 'incoming nukes' alarm at the base next door" to "the 10 cent chip sent random noise through the computer system and the system's memory register put that as a nuclear attack" to "we didn't realize a simulation was running" and many others). It's an interesting variation on the trope. I haven't thought about the difference between these types of "close call" narratives (individuals vs. systems). In the US, you have "it all came down to this one switch not failing" narratives (Goldsboro), but not "it came down to this one person" narratives.
One issue is that in the US, individuals have very little autonomy — there just aren't that many opportunities for an individual to make a call like this, because in principle the only individual who can make this call is the President. It's not been quite as neat and clean as all that over the years (there are ways in which, for example, the President can predelegate nuclear use authority), but it did, over the course of the Cold War, result in a different sort of attitude towards the role of an individual serviceperson in the nuclear forces. (The closest thing that comes to mind are the Cuban Missile Crisis negotiations, which could have gone different directions depending on who was in the room. The fact that this "human" factor involved the highest-level authorities is exactly the sort of thing you'd expect in the US system.)
It may, of course, be an artifact of other cultural tropes as well. The "heroes" of the USSR (notably Arkipov and Petrov) have probably had their roles inflated after the fact, as a way of illustrating how close "the brink" was, and as a way of sort of elevating the Soviet serviceman beyond the gray anonymity that comes with the nuclear complex.
Hmm. I'll have to think on this some more, because it's an interesting thing to notice. It interestingly inverses the usual Soviet-US technotropes — for example, in the Space Race, the Soviets mostly engineered cosmonauts out of the equation (they were only supposed to intervene if there was an accident or error), whereas in the US the astronauts had much more central roles (in part because digital computers could not automate everything at that point — the Soviets used analog computers that did better for the time). I'm of two minds on whether this is a "real thing" (the "systems" argument) or just a narrative trope difference. Something to mull over. (I am writing a long piece on Soviet nuclear accident narratives, so this is useful food for thought.)
If you are looking for stories of mishaps, false alarms, and close calls in the US program, Schlosser's Command and Control is full of them. Again, they focus less on people (at least, not in a positive way — the central accident Schlosser looks at, the Damascus incident, is caused by a guy dropping a wrench) and more on systems (e.g., the sort of thing where dropping one wrench can lead to a disaster). On the differences between the Soviet and US early space programs, see the work of Slava Gerovitch.
As for non-US, non-Soviet examples — very little comes out of other nuclear programs, so there very well may be variations on this that haven't been told yet. There are certainly "close call" stories from other nations, but verifying them is tricky, and they tend not to feature individuals.
There is a third, rather popular hero (also from Russia) from the 1960's at the height of the Cuban Missile Crises. His name is Vasili Arkipov. His decision averted a probable Soviet-USA war.
According to Soviet submarine officer who averted nuclear war honoured with prize (by the Guardian)
""A senior officer of a Soviet submarine who averted the outbreak of nuclear conflict during the cold war is to be honoured with a new prize, 55 years to the day after his heroic actions averted global catastrophe.
On 27 October 1962, Vasili Alexandrovich Arkhipov was on board the Soviet submarine B-59 near Cuba when the US forces began dropping non-lethal depth charges. While the action was designed to encourage the Soviet submarines to surface, the crew of B-59 had been incommunicado and so were unaware of the intention. They thought they were witnessing the beginning of a third world war.
Trapped in the sweltering submarine – the air-conditioning was no longer working – the crew feared death. But, unknown to the US forces, they had a special weapon in their arsenal: a ten kilotonne nuclear torpedo. What’s more, the officers had permission to launch it without waiting for approval from Moscow.
Two of the vessel’s senior officers – including the captain, Valentin Savitsky – wanted to launch the missile. According to a report from the US National Security Archive, Savitsky exclaimed: “We’re gonna blast them now! We will die, but we will sink them all – we will not become the shame of the fleet.”
But there was an important caveat: all three senior officers on board had to agree to deploy the weapon. As a result, the situation in the control room played out very differently. Arkhipov refused to sanction the launch of the weapon and calmed the captain down. The torpedo was never fired.
Had it been launched, the fate of the world would have been very different: the attack would probably have started a nuclear war which would have caused global devastation, with unimaginable numbers of civilian deaths.
“The lesson from this is that a guy called Vasili Arkhipov saved the world,’’ Thomas Blanton, director of the National Security Archive at George Washington University, in 2002, following a conference in which the details of the situation were explored.""