Overheard after the Georgia execution was stayed

Overheard after the execution of Troy Davis in Georgia was stayed:

"Holy crap, it's 2008 and we're not sure whether the 8th amendment bars the execution of the innocent?"

"Yep. God bless America!"

Link goes to Davis's petition for certiorari (40 page PDF). Basically, he argues that Georgia's capital case review procedures create a liberty interest in a new trial. Therefore, once Mathews factors are applied, it's beyond questioning that the procedures the state has in place are inadequate due process for someone who faces execution if the state denies a hearing on the issue of granting a new trial.