I've never heard any indication that Byrne was fired. He quit because DC wasn't putting forth his version of Superman as the definitive version outside the comics. But his reinvention of Superman remained in-continuity for over a decade afterwards, so DC certainly wasn't disowning his take on the character.
Nor did I ever get the impression that Byrne left on a controversial note to stick it to DC. I was under the impression that this was a story he'd planned to do anyway, and he would have seen it through its consequences had he decided to stay. As it was, the primary writer responsible for the ensuing storyline was Byrne's friend Roger Stern.
For those not familiar with the comics in question, the gist of it is that this was an attempt to address Superman's traditional code against killing by giving it an origin in the post-Crisis continuity, rather than taking it for granted as something that came with the character out of the box. Superman reluctantly executed three Kryptonian criminals as the only remaining authority on an alternate Earth where those criminals had destroyed all life. It weighed heavily upon him, and ultimately caused him to develop a split personality. While he became less effective as Superman, he was using more extreme methods in his alternate persona as a costumed vigilante named Gangbuster. When he came to his senses and realized what he was doing, he exiled himself from Earth. During the exile storyline he came to terms with what he'd done and firmly resolved that he would never kill again.
Some people here who obviously never read the storyline in question are making a lot of generalizations about it, when they simply don't know what they're talking about.