The run that died
The mistake is rarely the thing that ends a run. What usually ends it is the handful of seconds after the mistake, while attention is still sitting on what just went wrong instead of on what is in front of you.
An error grabs attention. That is what errors are for. Research on what happens immediately after a mistake finds that people reliably slow down, and that the slowing is not automatically useful. Some of it is sensible caution. Some of it is attention still stuck on the last thing rather than the next one, which is exactly when a second mistake tends to arrive.
Naming the error in five words or fewer is a way of closing that loop fast. Five words is short enough that you cannot rehearse it or start building a case against yourself. “Missed the clip.” Done. Then attention has somewhere to go, and the next checkpoint is a better destination than the next attempt, because a checkpoint is something you can act on right now and an attempt is not.
Twelve seconds is a joke about the format, not a prescription. Some mistakes deserve a proper think, and that think is worth having after the run rather than during it. None of this makes a run recoverable that was already gone.
Where this comes from: research on post-error adjustments, which finds that behaviour changes measurably in the action after an error and that slowing down is not always the helpful part (Danielmeier & Ullsperger, 2011).