Is BR out?

[Centerfield9]

The batter hit a deep fly ball to the outfield and dropped the bat into fair territory. While the batted ball was in the outfield, the on-deck batter moved the bat out of play. The umpires ruled that the BR is out because the on-deck batter entered fair territory during live play. Is that the correct call?

I understand that if the on-deck batter interfered with a play or intentionally tried to distract the fielders, the umpire could rule against the offensive team, but that didn't happen. The intent was to get the bat out of play to avoid a player (offensive or defensive) from getting injured.