You engage with the autistic guy at your own peril.
There's been enough ideas that have been around since the beginning of the sport (in pretty much every sport) that have turned out to be wrong that I don't consider that to be particularly useful evidence. Batting average is not the most important offensive stat in baseball. Defense doesn't contribute any more to winning championships than offense does. Conventional wisdom isn't always wrong, but it is wrong often enough that it's tough to rely upon.
That so many things have been shown to be incorrect despite "everyone" saying that they are important, that it's hard to know what to do with a statement that something "doesn't show up in stats but absolutely impacts wins and losses." Why should I find this convincing? As it happens, I don't find this case to be implausible, but I'm not sure that it gets you to where you want to go. Confidence is a fickle thing, and confidence in a particular goalie often isn't predicated on their ability as a goalie. It can come from personality elements. It can be based upon that goalie being "hot," but the problem with hot streaks is that they are descriptive but not predictive; it's easy to see in retrospect that a goalie is hot, but that doesn't tell you anything at all about whether they are going to continue to be hot. There have been a lot of studies on this, and they all say that the best estimate of how a goalie is going to perform in their next game is their save percentage over approximately the last 6,000 shots they've faced, and not how they have done in the last few games. (And, for what it's worth, no goalie faces anything close to 6,000 shots in a four year college career, which is why their career save percentage is so volatile.) Saying that it's important for a team to have confidence in their goalie is both unverifiable and not really a statement about the actual abilities of a given goaltender.
Sure. That happens. But the question is whether or not this is something that you can predict ahead of time, or only note after the game is over. To what extent is attributable to the quality of the goalie, and to what extent is it a combination of outside circumstances and a one day performance that is out into the right hand tail of the distribution of that goalie's overall performances?
Here's a piece from 538 that looks at the problem of goalie volatility and how that makes it hard to even figure out who the best goalies are. Obviously, it pertains to goalies at the NHL level, but the same basic problem exists at all levels. It at least partially disagrees with me offensive variation is more important than save percentage variation in winning games, though it breaks things down in a way that is hard to pin down one way or the other. At the same time, it argues even more strongly that a lot of what we perceive as goalie quality is actually circumstantial:
https://fivethirtyeight.com/features/a-hot-goalie-isnt-a-better-goalie/