I'm going to leave further back-and-forth on the narrative (and my armchair psychoanalysis) aside, and focus just on your question, since it's both interesting, valuable to understanding the game, and strikes me as answerable.
SI, May 2019
: Lots of coaches go on record talking about the times they've let it ride, particularly at the very end of the game, and seen players execute and win. D'Antoni asserts: "There are no analytics that really proves that if you call a timeout, it stops the run of the other team," he says. "Actually, there's evidence that doesn't support that." Or some other prominent names:
Vice, Dec 2015
So what about actual scientific approaches to the question?
Econ PhD Thesis on the subject
, 2011: "This paper explores the claim that timeouts enhance short-term performance following a series of negative events". It covered a sample of ~3700 games from 2006-2009. Its conclusions: once you control for the fact that a team calling timeout after giving up a run starts the next possession with the ball, and for home-court advantage generally, there is a small positive effect of timeouts for momentum-stopping purposes, with teams scoring ~0.5 more out of the next 10 points scored than the similarly-situated teams who did not call timeout. However, there's also plenty of mean reversion: teams who give up runs tend to outscore their opponent following those runs anyway
, rather than let it continue to snowball, as you would frankly expect with the results of possessions being fully stochastic.
arXiv paper July 2021
: these guys conclude the opposite, or rather, have a stronger conclusion based on asking the question better. Using what seems like a better technique, they conclude that letting players play through it is more advantageous than calling a timeout.
Based on those, I think we can agree that me drawing a conclusion in the other direction was largely bullshit. Thanks for sending me in that direction.