it's not a stretch to see how such an incident resulted in his eventually getting the vessel
Not a stretch, but still apocryphal. Also, we could just as well argue that Picard getting born resulted in his eventually getting the vessel; "Tapestry" lists two specific incidents that helped drive Picard along a steeply ascending career path, and this "taking command of the bridge when the skipper was out for the count" thing need not have been more decisive than the "away team saves ambassador" one.
Not that I'd absolutely object to the speculation based on the backstage bio. But it does seem to diminish Picard's character if he gets stuck commanding the same rust bucket for two decades, without any mention of major events that would punctuate the career the way several last-minute rescues of planet Earth, several cases of terminal boredom and resignation (figurative or literal), and several triumphant returns punctuated Kirk's.
Picard's bio is an attempt to give background to a man who is old when we first meet him. Realistically, then, it should be a complex collection of events and achievements, more so than the bio of a younger man. But even more realistically, it cannot be that, because this would be too much of a chore to write - so each achievement the writers invent is stretched out instead to fill the gaps in the story. And stretching a single captaincy to 22 years was a bad move...