Not to dismiss the potential severity of the North Carolina incident, but it seems like we're more likely to bring a nuclear apocalypse upon ourself through human error than engineering.

Exactly right.

Excluding the Cuban Missile Crisis, there have been a number of incidents where military men simply stayed calm in situations where radar and other equipment suggested every indication of an attack. Thankfully the psychology of mutually assured destruction kept those with their finger on the trigger thinking, "No, this cannot be right."

Quite.

I think the most recent was in 1995 when a Norwegian science experiment was mistaken for an incoming missile from the United States. Luckily the incident never escalated to Boris Yeltsin; had he been drunk at the time, who knows what part of the country would be a radioactive crater.

...it's a little more nuanced than that. One of the most frightening things about the Russian Coup was the already-fractious chain of command was broken into several pieces, all of which disliked each other intensely.

The Soviets built the Dead Hand because their own wargaming indicated that they lacked the command and control hierarchy necessary to launch against the US in retaliation against a first strike. The delay between a NORAD confirm and a decision in front of the President is 18 minutes; the Soviets knew that upon launch detect they couldn't get their shit figured out in under half a day. They also knew that if they gave authority to the people who could retaliate in time, there would be hundreds of dudes in bunkers with the ability to start nuclear war whenever they wanted (a bad thing in a managed economy with a conscript army). So they gave it to the computers.

To your broader point, Hollywood made Wargames into a movie. The USSR made the WOPRa reality.

IT'S STILL RUNNING