Whether "160 times more fat than Coca Cola" is a lot, dumping a whole carton of it into the bathtub would leave a thin layer of fat/oil residue if not cleaned properly. That was my point.
Also possible that, like notKaosu said, the brother was storing oil from something else in there (this could be common enough for the joke to land in Japan, or maybe it was supposed to be out of left field, couldn't say) My assumption is that it's just a quirk of the translation and the brother pointing out there's oil and fat in the milk.