Is it really the case that taking a good multi-vitamin can help cure acne?

No, but...: I'm among a minority of physicians who believe it's wise for everyone to take a cheap vitamin-and-mineral supplement daily, because of the way our world is. You'll also do well to get with a scientific physician; acne can be treated effectively, usually at little cost, and the medicines (vitamin a analogues, antibiotics) are mother nature's gifts.