Where does this 'creation' assertion fail? The proof establishes a conditionality, it does not create the equivalence of sensitivity between methods based on fixed points and KKT; it reveals it under specific assumptions.
The weak link is the implicit universality, because this equivalence only holds if equation (25) is absolutely valid.
For example, unforeseen changes in market conditions such as sudden illiquidity of assets are not captured by the mechanism and could render this theoretical equivalence invalid.
A proof describes a relationship, it does not manufacture it, especially without considering exogenous risks or structural shocks which, in the real world, break these elegant symmetries.