The idea that evidence can 'create' an equivalence is a concept I find not very judicious; it discovers and formalizes, but does not forge existence.
My a priori is that the equivalence of KKT sensitivities is contingent on very specific, often idealized market conditions.
For example, adjustments to the regulatory coefficient on capital or changes in liquidity criteria could invalidate the underlying assumptions, making this theoretical equivalence obsolete in the practice of hedge funds.