It's quite ironic what O'Connor wrote in her concurrence: "the execution of a legally and factually innocent person would be a constitutionally intolerable event," while simultaneously voting to make it even harder to prove one's innocence.
While I suppose one could argue that this was an example of the maxim "bad cases make bad law" one thing that is abundantly clear is that as O'Connor wrote "Petitioner has failed to make a persuasive showing of actual innocence. Not one judge—no state court judge, not the District Court Judge, none of the three judges of the Court of Appeals, and none of the Justices of this Court—has expressed doubt about petitioner's guilt. Accordingly, the Court has no reason to pass on, and appropriately reserves, the question whether federal courts may entertain convincing claims of actual innocence. That difficult question remains open."
Even had a new trial been granted and the new evidence admitted alongside the old, there's no reason to conclude there would be any difference in verdict. The only way there would be is if some of the old evidence could no longer be presented because of the passage of time. Herrera was a justly convicted guilty party.