I am not sure if its as relevant today, I have not seen skin care with the 'bad' alcohol in it for some time. But then, I only ever use professional quality skin care, never any cheap stuff.
In the past, skin care particularly toners had alcohols to assist remove excess cleanser as it was quite popular to use 'cold creams' which were thick, greasy creams, to remove make up. But that was many years ago.
When I was a teenager, I used a toner from a pharmacy that had alcohol in it to treat my acne. Not only did it dry the skin out, but my skin got oilier and as a consequence the acne got worse. So perhaps there are still some acne products around formulated with alcohols. But generally good skin care products no longer contain the drying type alcohols.
There are certain alcohols used in formulations that are actually beneficial to the skin. Here is a very interesting article on the type of alcohols to avoid, especially if they are towards the top of the ingredient list. And a list of beneficial alcohols used in skin care.