I think it's a problem of communication, words get missed out in everyday language. If you take these words (*and only* these words) literally then of course "a pound" of anything weighs the same as "a pound" of anything else - de facto, by definition.
But what your consultant was trying to say is that if we compared, say, a handful of fat to a handful of muscle (ie the same volume) the handful of muscle would weigh more. A handful of potatoes *weighs more* than a handful of lettuce. Of course "a pound" of potatoes and "a pound" of lettuce *weigh* the same - but "a handful" of each *do not* weigh the same because they take up a different amount of space as they have different densities.
But this is kind of defeating the motivational point of trying to explain it in the first place if you don't see the point so Im leaving it there