Is this any different than an umpire who loses the count insisting he's right despite everyone there knowing he's wrong? If an umpire says it's 3-2, it doesn't matter that the girl fouled off a pitch, took a strike looking, and then swung and missed. It's 3-2. (And lol at the idea of him deferring to the home team's scorebook)
If an umpire says there's three outs, if he feels like sticking with that, he can. It's a "point of fact," but if an umpire wants to make up facts, they can. They have. I see it more often than I should.
Establishing the number of outs is easy. Observers, even scorekeepers, don't always keep accurate track of a batter's count, but coaches and scorekeepers on both sides can quickly and unambiguously establish the number of outs. I've seen a single umpire momentarily confused and consult the Home scorebook. If the other team objected, they would need to produce their own for comparison. If I have a well kept scorebook, and especially if there are opposing scorebooks that agree, and the umpire won't budge (never seen it), I'm calling the TD/UIC over to discuss. I'd bet money on the outcome.
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