Well, the conveniently indicated grams on the packet are not units of weight - they're units of volume. So you've got two kinds of units of volume in your recipes: milli/centi/decilitres, and grams of butter. But it's fairer than the grams of flour I've been ranting about elsewhere here because at least the manufacturer can have some responsibility for fine tuning it to their product!
They are the SI unit of mass. He's just saying that because it's indicated by lines on the package that the actual measurement is done in volume, and the conversion is implicit by the scaling. Where he goes wrong is in thinking that it's implying that "grams of butter" is a unit of volume.
The exception is usually butter, which is measured in grams (and conveniently indicated on the packaging).