This is a little wooly, since there is a perfectly legitimate sense in which the brain is not sufficient for life. We have to have some functioning method for breathing and obtaining nourishment, for example.
And, there is some need for clarification of what kind of necessity and sufficiency one is talking about.
But, the neuromuscular blockade stuff shows pretty strongly as far as I can tell that the brain is a minimal supervenience base for consciousness, as opposed to life. The only reply I've heard to this observation is that the neuromuscular blockade results do not show that the brain alone is that all conscious states.