The reason why I don't usually mention zinc in discussion of acne is because it is a trace mineral and most people get enough dietary zinc. Anyone who eats two servings of beef a day (or one typical restaurant portion) gets about 12mg to 15mg per day. One could also get that amount from 12 ounces of almonds or cashews (now you know why you eat the whole bowl of nuts, every time).
Outside of people with a condition like yours, only vegetarians and anorexics would tend to have need for supplemental zinc.
Of course, if one has diarrhea, ulcerative condition, or lives in a cold climate, one could be in need of extra zinc. If one is eating a certain way, one can either reduce the bioavailability of the zinc one does get (and thus increase the amount needed to make normal use of it.
I do thank you for bringing it up, however, as there are in fact some people whose acne problem would be zinc based, and nothing more, just as we often see people whose unwanted hair problem is based solely on their use of artificial sweeteners, and the side effects from that chemical reaction inside the body (IE; Hormonal Imbalance, insulin resistence).