I apologise in advance for how long and wordy this post is....
I read this thread a while ago and I see that it is still going. As painful as it was I have finally watched the whole video, I thought I would spend a minute or two going through my take on it. My first thought is that he has a very poor understanding of basic immunology.
He claims that evolution has made us a perfect human machine. Implying that inflammation is a perfect response to all injury. This is not true. The body has trouble telling the difference between, for instance, an infection and tissue trauma from say a sprained ankle.
Acute inflammation (ie from neutrophils) is a non specific reaction which causes reasonably indiscriminate destruction of an area. This is great for things like infection where you want to destroy a pathogen even at the cost of destruction of native tissue (at least as a stop gap measure until the adaptive immune system can be mobilised). It is not so great if there is no pathogen and only your own tissue that is getting destroyed. Evolution doesn't really care about this too much as you don't usually die if your immune system causing a bit of extra destruction from a sprain, whereas you may die if your body can't get on top of infections quickly.
Luckily we ourselves are able to tell the difference and can modulate acute inflammation depending on the cause. Eg steroids injections are amazing at reducing inflammation from musculoskeletal injury (eg this can be great in lower back pain to prevent a chronic pain syndrome) but you would definitely not want to inject steroids into an infection.
Ice is good for reducing acute inflammation and stopping neutrophils degranulating and releasing destructive chemicals. Once the period of acute inflammation is over (and the number of neutrophils in the area has decreased) heat is good for promoting removal of damaged tissue and supplying nutrients to the area promoting healing.
He talks about swelling and how movement of muscles gets rid of the extra fluid through the lymphatic system. The reason you get swelling is that inflammation causes increased permeability of capillaries in the area causing more fluid to leak out into the interstitial tissue. Sure, movement and TENS will cause extra movement of fluid through the lymphatic system but it is effective to use anti-inflammatories to not only reduce neutrophils destroying tissue but also decreasing the amount of fluid leaking from the capillaries into the interstitial space (This is a key concept he does not understand).
In terms of rest and ice
* Rest is important, they even say you should not do enough movement to cause additional injury to the area. Sure a little bit of movement is fine but the point of the R in RICE is that you should not push yourself too much after an injury and cause more inflammation.
*Ice, he says ice will cause more congestion of interstitial fluid increasing swelling, this is wrong. Ice reduces inflammation which decreases capillary permeability thereby reducing swelling. The reduction in fluid leakage into the tissue is greater than any "congestion" they claim. Yes, icing will slow down the healing process because you are not clearing damaged tissue and not getting nutrients to the area HOWEVER it also reduces tissue damage caused by acute inflammation which is more important (this another key concept he is missing). In the ideal world we would stop the destructive aspects of acute inflammation and only have the positive healing effects increased blood flow but we are yet to cheaply and effectively achieve this. Instead we reduce inflammation and then let our bodies move onto the next step which is healing and regeneration, we can also artificially increase blood flow at this later stage eg using heat packs a couple of days after the injury once inflammation has subsided to further promote recovery.
He says that in the phases of healing, inflammation is the first step and that by stopping inflammation you halt the healing process. This is simply wrong, sure a little bit of inflammation is required to get rid of damaged tissue but a lot of inflammation causes more harm than good. You can curtail the inflammatory response and still have excellent regeneration and repair afterwards.