Yes, and with planes. It happened to the Germans all the time as the UK spoofed commands by the ground controllers. We also played with the guidance signals coming out of Nazi German for bombers with fake signals. I don't remember the corp number, but one Soviet Corp fighting Army Group North in the summer of 1942 was dealing with the Germans constantly spoofing the codes, and the corp by mistake cut off communication with the Soviet Army. Both sides were using the same authentication codes. I am sure there are a lot more examples. A key point is that code books do get lost. Spies do compromise codes. Sometimes the bad guys just break the codes. And the guy who did the spoofing had done that as his job in the regular army, and he believe not only in a war would people try, but people would succeed. He believed both sides would have success, both NATO and Warsaw Pact. Both the USA and USSR had full time military intelligence officers who knew more about the enemy forces than the average Colonel in command. There are people who are brought into the military complex trained only to think like an enemy officer.
And you comment on using real authentication procedures is why bringing the wife on to recall the bomber does not work in most cases. Most of the time someone would try a stunt like this, it is the enemy, not your friend. If I am at SAC with the real code books, there should never be a reason not just to use the code books. The reason I gave the story is to show what happens when you start ignoring the procedures and designing radio procedures on the spot. You normally end up with massive security holes that the enemy can exploit. The sister battalion had code books, but got lazy and decide not to use them, for whatever reason.
Now the premise of the movie is that after a certain point, the Air Force had determined the odds of a false soviet signal was too great to allow the Air Force to attempt recall orders. While for plot devices, I would have chosen a different method, I think the movie is plausible. Let us look at some possible issues. First, as you approach Soviet territory, you are likely jammed and can't communicate. It is easier for the Soviets to send you radio message than the USA since the Soviets control the jamming. The USA knew the Soviets had good spies that often had big successes. The Soviets had stolen big pieces of the Manhattan project, so it is possible to think they might have SAC code books. There was the Cambridge 5. During Able Archer (1983), the Soviets had access to the information in the most secure NATO room. The also knew the frequency used for a real nuclear attack, and might have the the actual command codes. The Walker family gave the Soviets US Navy codes for over a decade. The only missing piece is a USA Radio or a Soviet Radio that can mimick the USA radio.
I can easily see the Soviets sending out fake recall orders using real authentication codes. I can see them working some of the time. I can see the Soviets spying on the family of bomber squadron commanders to get a few tidbits of information, so they could put out fake wives. How hard is it to get an agent into a country club or hair salon near a SAC base? Compared to getting in NATO most secure room. For that matter, if you can get spies into the Manhattan project, why is it a stretch to think they might have one at SAC HQ? I would expect SAC would know that the USSR was constantly trying to spy on the program, and become more worried about a spoof than a fail-dangerous command. So I find the movie plausible.
Redundancy in MAD was not a case of making sure that once the Bombers went up they couldn't be called back, that would be crazy, since getting the bombers up would be one of the last steps in deterence. It was a case of having multiple launchs vectors. In the 60s ICBMs would be the primary weapons. I am not familiar with SAC codes, and expect what is avaiable online and in bocks to be falible, but I would expect something along the lines of one time pads issued at take off. Those are very hard to break, unlike simpler to break encryption codes used in voice radio to rapidly encode mission orders.
During WW2 the mains problem was jamming, and in fact the LW had at one time to ressort to having the pilots tune in to music broadcasts and follow the "if its Bethoven they're over Berlin" method.
It's the double premiss that a. Nuclear attacks can be launched by mistake and b. once launched they can't be called off that I find manipulative.
The wife thing is clearly just a bad plot device to get a dramatic response. Not the thing you'de have time to do. Of course you can have the pilot say to his crew "damm, even my wife his a commie spy, lets nuke those devious bastards" but plausability just gets thinner and thinner.
Dr Strangelove worked because it was pure satire, starting with the "doomsday device" idea to really generate Totally Assured Destruction...