I've never heard of muscles breaking down proteins, nor have I ever heard of proteins causing liver damage (that doesn't make any sense).
Muscles do release lactic acid, which will eventually cause enough pain to make you stop, but I never heard of any serious damage caused from it. And this cooling method won't prevent that feedback.
It's obviously possible to inure a muscle, but it will hurt, and this cooling method won't affect that.
http://www.nlm.nih.gov/medlineplus/ency/article/003503.htm
The part about muscles releasing proteins when working out is definitely true, I just don't know about the rest. It's something I was told by my sports doctor though.
It's usually caused by crush injury, but if you're enough of a knucklehead, you can give it to yourself in the gym too.