I don't know about evidence to prove it
but I can say for myself, that even WAY beyond my teenage years, when I did the no starch diet, my skin improved big time, in about a month
as a teen and someone who who had trouble with acne ever since, I always heard people saying that chocolate, oily foods like pizza were the problem
but NEVER tried avoiding starches like bread, rice and pasta, it just didn't make any sense to me
but that's exactly what happened when I did the NSD, and have read in a few places that it worked for others too
so consider that as something to try, I so wish that I could have tried it many years ago!