Simply put, it wasn't the Court's job to exonerate Davis. In a 2009 decision on the case, Justice Scalia wrote, "This Court has never held that the Constitution forbids the execution of a convicted defendant who has had a full and fair trial but is later able to convince a habeas court that he is 'actually' innocent. Quite to the contrary, we have repeatedly left that question unresolved."
William Baude, writing in the Fall 2010 issue of The Wilson Quarterly, explains how our already lengthy appeals process simply cannot be stretched, last minute, to set a man free:
At a trial, the government is required to prove beyond a reasonable doubt that the defendant is guilty. If he is acquitted, that is the end of the matter. If not, he can appeal to higher courts, and ultimately ask the U.S. Supreme Court to review his case. If those appeals fail, he can challenge his conviction again by seeking a writ of habeas corpus (a form of court-ordered release) in both state and federal courts.
Yet what if someone goes through every possible procedure and after all is said and done still claims to be innocent? What if another court were to actually find him innocent? No belated claim of innocence has yet been found so compelling as to force the issue...
Congress, for its part, has said that a convict has only a limited number of appeals and opportunities to attack his conviction in a federal court, even if he has new evidence.
There is no precedent for the court to save a death-row inmate last minute, and the law of the land places a limit on appeals. Instead of approaching this as a judicial matter, Baude says Congress should enact new laws that create a finer balance between "never-ending reviews" and reasonable doubts. Obviously, there has to be judicial finality: otherwise the courts would be so busy they would be rendered useless. But whether Davis should have received yet another review is a question for lawmakers. Baude writes, "Judges cannot simply answer [that question] by saying that there is a duty to get it right, regardless of how many proceedings and how much time it takes, because the judicial system's resources are finite."
So while lingering doubt may seem like a powerful enough reason to stay an execution, in the intricately complicated world of the justice system, it's just not enough.