Holy cow. What she is actually doing is pissing her zits off and they are rebelling by multiplying! Irritating and drying out her skin will only encourage sebum production. I used a buff puff as a teenager and it never helped.
Unfortunately all the creams and soaps and scrubs most likely won't make them go away (although the scotch pad WILL make it worse!). It is likely hormonal so while proactive and other such products might help control it A LITTLE BIT, gentle cleansing (with fingertips!), proper moisturizing and BP or salicylic acid treatment (or aspirin mask spot treatment) is the simplest and most effective for most. You don't have to spend a lot of money!
Also, a low cost minocycline or doxycycline can be miraculous!
I have a 16 year old daughter with normal teenage acne (she thinks its horrible, of course. She says she looks like a troll. She is NOT a troll. goofy girl (***an aside*** I made her a cp face soap and I call it "Troll soap". haha. Still curing so I'm not sure about it yet.)
The best treatment we have found so far (and we have tried them ALL) is the aspirin mask. Seriously. The best. No joke. check this out....
http://www.acne.org/aspirin-mask-reviews/75/page1.html
Or just google it. There is tons out there on it.
We use crushed aspirin, a splash of witch hazel, a squirt of honey, sometimes some plain full fat yogurt, sometimes aloe gel. Basically just make it into paste that will stick with face loving ingredients. I want to incorporate some french green clay in there sometime.
Obviously she should never, ever use anything that is a comedogenic.
acne.org is an awesome resource by the way.
Good luck!!