It is the right answer with the wrong explanation. Mass and weight are two different physical quantities. Weight is the resulting downforce acting on a body on Earth. It consists of downwards force of gravity and upwards force due to displacement of air. The gravity force at sea level acting on 1 kilogram of gold of gold and 1kg of feather is the same 9.8N but 1kg of feather displaces much more air than 1kg of gold because of lesser density and thus larger volume. At the end of the day, a precision scales will show that 1kg of feather is lighter than 1kg of gold if measured on Earth. Of course, LLM misses all of this phycics :-)
EDIT: On the Moon with no atmosphere 1kg of gold and feather will weigh the same.