Catalysis of the reaction: (3S,4R)-3,4-dihydroxycyclohexa-1,5-diene-1,4-dicarboxylate + NAD+ = 3,4-dihydroxybenzoate + CO2 + NADH.
(1R,2S)-dihydroxy-3,5-cyclohexadiene-1,4-dicarboxylate dehydrogenase activity