I teach my dd and other catcher to do it your way. Her first move is right foot crosses behind her left foot with instep facing third and throw off that foot. It a big enough step back to easily clear the batter and the throw stays on the foul side of the baseline.
Dd always argued for your dh's point, we were watching a 16u game and the catcher just drilled the batter in the helmet with the ball. Batter was fine but the ball flew almost to first base and the runner scored.