I've read the case and I don't think I'm over-reacting at all. There seems to be a serious disagreement of fact between the justices as to how substantial this person's likelihood of success is. Its impossible to evaluate without more information. But thats not wants important. What's important is the underlying question of whether a person who is actually innocent must be executed because the procedure says that is what is supposed to happen.

Scalia certainly seems to welcome that debate:

If this Court thinks it possible that capital convictions obtained in full compliance with law can never be final, but are always subject to being set aside by federal courts for the reason of “actual innocence,” it should set this case on our own docket so that we can (if necessary) resolve that question.

As I previously stated, there should be no debate about that. The answer is yes.

Stevens writes:

Imagine a petitioner in Davis’s situation who possesses new evidence conclusively and definitively proving, beyond any scintilla of doubt, that he is an innocent man. The dissent’s reasoning would allow such a petitioner to be put to death nonetheless. The Court correctly refuses to endorse such reasoning.

Good.