If agents are morally required to seek correction of reasonably suspect beliefs, then a merely subjective judgment of conscience is not automatically binding in the manner the claim asserts.

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Subjective judgment(epistemology/ethics): A decision or determination made based on personal opinion, feeling, or perspective rather than objective facts.
automatically(as used in logic and philosophy): Happening without question or without needing any additional conditions; something that just applies by default.
binding(Binding theory of presupposition): The linking of a presuppositional expression (including pronouns) to an already-available discourse referent in the DRS.
conscience(Aquinas' account, distinguishing conscience from any special moral sense or indwelling presence): Not a special power or faculty within a person, but practical intelligence at work — primarily in the form of a stock of judgments about the reasonableness (rightness) or unreasonableness (wrongness) of kinds of action.

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