Hinch moving Bregman had 0 to do with it.
The Red Sox played horrendously in Game 1 and lost. Seriously, 10 walks and 3 hit batters would make it hard to beat Baltimore in mid-July.
The Red Sox played better in Games 2-5 and won. The Red Sox were relentless offensively - not giving away outs. The bottom of the lineup - the real weak spot of this team all season, came through. Bradley and Devers had great series, and the catcher position was never a serious drag on things.