Do you know who has such shitty skin they are trying to drown themselves in acne medication? 13-year-olds. Do you know who should not be given a big ol' jar of ethanol? 13-year-olds. Denatured alcohol is just alcohol that has shit added to it to make it disgusting. People were worried that teenagers would end up drinking their toner or whatever and they'd end up drunk, poisoned, or both. In cosmetics, you'll usually find denatonium.
Alcohol that has been denatured isn't subject to the same sorts of sales restrictions and taxation laws as traditional ethanol.
It's definitely worth noting that there are also a few reasons why denatured alcohol might not be the most attractive option for skincare products aimed at acne-prone skin. In some individuals, alcohol can increase the irritation caused by the acne medication itself. There is some in vitro evidence that alcohol might trigger apoptosis (cell death). And, of course, there is the reality of homeostasis: if you rely on alcohol to dry out your skin, you'll end up producing more oil to compensate. In light of this, I would consider alcohol to be an undesirable ingredient in a lot of skincare, particularly in products that go directly on your face. (Conversely, it might be a benefit in products that go on top of a shitload of other products, since it will dry up all the extra crap, rather than drying up your skin.)