In that case (fascinating reading!), the person used far too cold of a solution, applied it for too long, and in consequence suffered a really bad injury, possibly compounded because she didn't seek treatment for 2 and a half weeks. Also, it was on a forearm, not the head or other hairy areas, so the mechanism of marking was more "kill the whole skin" than "kill pigment cells" specifically.

It could be done in a much safer manner - I don't think it really proves much about effectiveness overall.