Not really, I had a friend at Nokia maintaining old code in a team. He was the go-to person for many years without getting promoted to even team leader position.
I told him to learn some new language that's used in the company that can be used as a leverage to switch companies as well if he isn't getting promoted, and try to switch. 1 year later he's working on writing new application load balancers in go, and he's loving it, and getting more money for it, and he can easily switch to other company if he wants to.
Of course the old team really misses him, but they didn't value him high enough, so they lost the best person on their team.
I don't consider your anecdote to be a valid argument against his claim that this is survivor bias. I appreciate you sharing that person's story but the fact is, there are many variables at play.
I think that in most cases, career advice is subjective and to brand advice as black and white, good or bad, is silly. Nobody can predict the future. A seemingly negative decision could potentially lead to other positive outcomes. That's why I find little value in this discussion: it's subjective and difficult to measure.
Sure, it really depends a lot on the situation. Jumping around is just as bad as rotting in a place, but I wanted to share my example because it was a clear cut case when my friend tried everything to fix the local situation first.