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There is nothing in the KE or momentum formulas that takes stiffness into account.

However, he does have a point. An arrow that's underspined will not absorb as much energy from the bow, because some of that bow's energy will be used up by making the arrow flex. It will also enounter more wind resistance as it worms around in the air before it stabilizes, which bleeds off some of the energy it does take from the bow. Not to mention terrible accuracy.

An overly stiff arrow will not flex as much and it will stabilize sooner, which will give it better energy than the underspined arrow. But, again, accuracy becomes an issue.