Fix the cause of your pain rather than conceal the symptoms?
Ice will slow(not stop) the inflammation. The natural inflammation occurs to promote healing of the area. So, the ice will delay the healing and conceal the symptoms of injury, not fix anything.
http://sock-doc.com/2013/02/recover-prevent-injuries/
Additional info of symptom relief: This is why drugs like NSAIDS are horrible in these cases, as it will break the healing process of the tissue and cause scar tissue. It greatly stunts tissue regeneration (inhibits fibroblasts (cells that regenerate tissue) and macrophages (cells that clean the waste from area))
http://www.caringmedical.com/sports-injuries/nsaids-why-we-do-not-recommend-them/
I am seeing this more and more, especially in the Crossfit community. There seems to be new phenomena that we are completely throwing RICE to the wind and letting the body heal "naturally".
I think this is a gross misinterpretation though. As healthcare professionals, we have to be careful how we word things and make sure the patient and others listening to our advice fully understands what exactly it is you're trying to explain. For instance, when you cut yourself, you will bleed. It's natural, right? However, too much bleeding will cause anemia, and even death. "But I thought it was natural!". Same with swelling. SOME swelling is ok, but too much swelling will NOT allow rapid or efficient healing. Remember that, also, there is a standard of care. If you have a patient that has swelling, and you don't treat it appropriately according to the standards of care because of some newer information that hasn't been established yet as standard of care, you can get your ass in some hot water.
BTW, using the RICE method isn't concealing the symptoms. If ice makes it feeling better, then it's been shown, with well backed studies, that it is treating the problem.
On a final note, I tell people to use ice for 24-48 hours, then use whatever makes it feel better after that. Pain relief using heat or ice IS treating the issue (Pain caused by inflammation, which prevents proper range of motion, possible impingement etc. If it's an infection causing the swelling, well, that's a different story. Antibiotics are needed in that case, not heat or ice.