Thanks for the conversation starter.
I come at things from a business analytics perspective, and this article pretty well encapsulates the attitude I saw across 35 years or so. An airline for example might use a form of analytics to minimize crew costs when scheduling their fleet for a month, and might have to use the same tools to recover when a snowstorm snarls their schedule. In neither case would they simply turn off their brains and rely on the output from the computer without incorporating their significant expertise in their own industry; before the advent of software powerful enough to address the problem, they had plenty of heuristics they used to get quite-good solutions. But in the first case they have the luxury of looking at the minimum-cost solution and seeing whether they can improve robustness or union satisfaction or a multitude of other factors, while in the other case they may be willing to take "any" quick and dirty solution the software offers quickly rather than wait for a truly minimum-cost solution to fix the immediate problem (the algorithms being quite time-consuming if allowed to run to completion), tweaking minor logistics issues by hand if necessary.
A big thing baseball has in common with airlines is fuzzy data and huge uncertainties. Airlines deal with uncertain demand, can be hit by weather (as mentioned), and small random delays can have a cascading effect on a schedule.
I don't have a similar inside look at what baseball teams do, but from the outside looking in, I don't detect nearly the arrogant analytics point of view that gets attributed to them. The Twins analytics representative who spoke at a panel discussion at the SABR national convention in August described the team's approach as analytics-assisted. That's how industry looks at it too.
One fun tidbit from that panel was the insight that after every game, Rocco and the analytics team go over the ways that he deviated from the plan going into the game. People on the outside call that plan a "spreadsheet" to be disparaging, but the point is that Rocco routinely deviates from it (multiple times per game, it was implied), and the analytics team wants to understand. Not the other way around.
Of course, I could be projecting my own approach onto what they said. 😀