Muscle does weigh more than fat, by volume. Of course a pound of anything weighs the same as a pound of anything else. I don't suppose anyone would argue that feathers weigh less than a bowling ball, but obviously a pound of feathers weighs the same as a pound of bowling ball. The only way to compare is by volume. If you control for weight (look at a pound of both) the measurement is size. A pound of fat is bigger than a pound of muscle.

It's all the same as saying muscle weighs more than fat.