After shopping around a bit, I found their website and saw the bold claim that they can repair my Samsung S3's screen for $99. I brought it in and sure enough, even though my phone's glass had been completely shattered into little pieces, Clean Planet completely fixed it! I am very happy and it is great to have a like-new phone again.
I'm not sure on the protocol, but I tipped the guy a few bucks too because the other place across town wanted over double for the same service.