I'm guessing he means keeping forearms and wrists still, and articulating from the lowest joint in your fingers.
It's one way, certainly, but it does not mean it's the only way. Sometimes when playing piano, we want to put a lot more weight into a chord. That's not easy just using fingers. So we may use the weight of the whole arm, and actually play from the shoulder.
Playing faster chords with the same shape for the fingers - as in eighths on, say, C E G then D F A, there's no better way than keeping the hand locked, and articulating from the wrist.
When playing faster runs ( I know you mentioned chords), then playing only with fingers and thumb works well.
And just because one method works for someone does not mean it will always work for another. If he was my teacher, I'd be questioning him about it. Teachers are not always right (I know - I am one!) and sometimes go blindly on, not really considering other options for what they do, in somewhat blinkered manner.