To anyone who actually read the FAQ on that site, they are not claiming that their sugar doesn't contain carbon. Their choice of terms may be unfortunate, but they clearly state that their use of "carbon free" is intended to mean that the product has a neutral carbon footprint.
I remember my HS chemistry teacher had some sort of food product with the label "chemical free." Things like that, and this, are amusing, but let's not pretend that the people who made them actually thought there were no chemicals (or carbon) in what they were making. That's simply not the case.