When a pitcher is able to throw near the edge of the strike zone reliably rather than sending fat pitches right over the plate, it makes it that much harder for batters to decide whether to swing, and that hesitation leads to more strikes. Sure, batters might feel inclined to blame the umpire, but it's just plain good pitching.
The strike zone might have been a little generous but it has been proven it just wasn't one sided. It has also been shown that left handed hitters were not affected at all by the strike zone. Right handed hitters where barely affected. The score was 3-1, hardly a blow out which proves it did not affect either side.
Dale Scott's generous strike zone was consistently bad, but both sides suffered equally from his poor judgment. Ultimately, the team that won was the team that was better in that particular game, i.e., the team that did not have to rely on an umpire getting all the calls right. Dale Scott did not favor one team over the other. He favored pitchers over batters.
Rarely is any one game decided by just one event. The strike zone does vary depending on the umpire, but as long as he maintains a consistent strike zone the players can adjust. The main problem with Dale Scott's strike zone is that it was not consistent. In addition, the game was also decided by plays made (or not). So while the generous strike zone is part or the reason why they lost, it is not the only reason or even the primary reason.