I would revise this to say "Don't JUST listen to what people say, watch what they do."

It's still important to listen to what people say.

Example: If someone yells "DUCK!" at you, it might be because something is headed right for YOUR head but not theirs.

Example: Quadriplegics can talk but can't do much else.

Yes, actions speak louder than words. Some people say they're going east, but their feet go west. Feet are more honest than words.