Before we go buying rope (which I'm passing no judgment on its usefulness in this or any other case) ...
Consider that we have the Judges our Presidents nominated, with the approval of our Congress ... all of whom were ostensibly elected by we the people. And we the people are less and less Constitutionally literate, and more and more self-absorbed. If our great great great grandparents knew how we voted, they'd take us to the woodshed. Their great great great grandparents dragged Blackstone and the Bible across the prarie; how many people here have read Blackstone? The Constitution is an amazing work, clearly articulating the deontological natural law beliefs of our founder, but it only works if the people today share those beliefs. Otherwise it becomes irrelevant, and we elect Presidents and Congressmen for whom the document is meaningless, and they nominate and approve Justices for who the document is meaningless. And people only complain when their pet project is threatened. ("Who needs more than 5 rounds in a rifle anyways? Quoth the hunter.")
Scalia's position reminds me of Micro$oft Technical Support - accurate, but useless. It is accurate to say that the Constitution does not address this specific case; its a document to protect the rights of the people. It would've been assumed, under natural law, that at any time innocence was determined, man's inherent right to life would trump everything else. The Constitution was not a collection of laws, it was a body of limits against the usurpation of natural laws - the right to life being the most basic. So yes, it doesn't say what to do when innocence is determined by a habeas court, but it shouldn't have to Mr. Scalia. Were we not at one time a nation that believed its "better that ten guilty persons escape than that one innocent suffer." (which is called the Blackstone Ratio)