> I suspect that only a minority of people in metric-using countries -- those with basic chemistry knowledge fresh in their mind -- know that

This is not the case. This part: "one milliliter of water occupies one cubic centimeter, weighs one gram" is known by most people, even kids in primary school. In other words everyone knows that a litre of water weighs one kilogram, and that there are 1000 litres in a square metre. I concede, though, that at least in Italy, which is the country where I was born and raised, most people wouldn't know the next part: "and requires one calorie of energy to heat up by one degree centigrade".