I don't know about that, I just finished War of Jokes & Riddles and he did try to kill the Riddler.
Also I just realized the Him that kept being referenced in the early part of the run is the Joker because of Bruce's attempted murder of the Riddler, I always thought it was the memory of Thomas Wayne based on the letter Bruce received during Flashpoint.
Also in the very beginning King laid out his thesis: Batman is Batman because he cannot stop, and Thomas is his rival, his antithesis.
Bane was his dark mirror because he too couldn't stop being Bane.
Pretty amazing