I would have thought you were right, but according to baseballrulesacademy.com we were both wrong. They say, "To qualify as one of three consecutive batters, the batter must complete his plate appearance, which ends only when the batter is put out or becomes a runner. If the offensive team is put out prior to any substitute pitcher completing his first three consecutive batters, the pitcher may be removed from the game between innings; but, if he returns for the subsequent inning, he must complete pitching to as many batters as necessary to satisfy the three consecutive batters requirement, which total would include any batters that completed a plate appearance with that pitcher the prior inning (i.e., if he completed 0 PA in inning 1, he must complete 3 PA in inning 2; if he completed 1 PA in inning 1, he must complete 2 PA in inning 2; if he completed 2 PA in inning 1, he must complete 1 PA in inning 2). An intentional walk counts toward fulfilling the number of required batters. Picking off a runner does not fulfill the minimum batter requirement, but would permit the early removal of the pitcher if the out recorded by the pickoff ends the inning."