The idiom has two meanings. The first with regard to people means to deal a hurtful metaphorical blow. From The Hamiltons, Or, the New Aera by C. G. Frances:
Yet, trivial as were these remarks, and careless the tone in which
they were uttered, not a syllable but cut right to the heart of
The second with regards to issues or problems means to illuminate the the basics with regards to those issues or problems. From The Limits of Empire by R. J. McMahon:
He cut right to the heart of the matter, observing that "we could
not alienate them in the Orient and expect to work with them in
The speaker is Cordell Hull, the Secretary of State under Franklin Roosevelt talking about the difficulty of dealing with European powers about their administration of their colonies in the southwest Pacific.
The first meaning is appropriate here. The Dreyfus Affair was notorious scandal in which antisemitic members of the French military falsely accused a Jewish captain in the French army of espionage. The scandal created a deep wound in French society, which was split into two camps of bitter enemies, the dreyfusards and the antidreyfusards.