If I read this right, much of the weight reduction is because a large component of the electricity-generating reaction is already plentiful in the atmosphere, s

If I read this right, much of the weight reduction is because a large component of the electricity-generating reaction is already plentiful in the atmosphere, so it doesn't have to be carried around with the battery. But as the battery is discharged, the oxygen molecules are altered (according to the video) and presumably stored in the battery - which implies when discharged, the battery gains (significant?) mass. During charging, the oxygen is released again, so the weight goes down. Is that right?