Unfortunately, most people don't understand what a chemical is and so businesses have to use shorthand in order to get it across that their products don't have any harmful chemicals in them. Too many people are anti "chemical" without even knowing what it means. Meanwhile, many people also love "natural" stuff, as if natural things aren't made of chemicals! Not to mention "natural" often includes citrus fruits, which as we probably all know by now from me complaining about them, have phototoxic properties. Some people are more willing to using straight lemon juice on their face than niacinamide or an AHA/BHA, because it's "natural".
They probably just say "chemical free" because it's the same way as saying "all natural" in this day's business-speak, and they already used "all natural" for the Nature box.
That said, I love the idea of the zero cosmetics box, I just figure it'll have a bunch of citrus based products I won't use.