A three-leaf counterexample for Fitch reconstruction under a molecular clock

Does Fitch parsimony on a tree whose leaves are all the same distance from the root reconstruct the root state at least as accurately as any single leaf? We give a negative answer for the symmetric twenty-state model. A rooted binary tree with three leaves and strictly positive edge lengths has Fitch accuracy $38829/400000$, whereas each leaf agrees with the root with probability $39/400$. The strict deficit is $171/400000$. The proof is an exact calculation over four types of Fitch set and includes uniform final tie breaking.