He’s talking about post-conviction procedures, and one thing to note is that at the outset he’s saying “this Court has never held…”. Which is true. It hadn’t ever done exactly that. So on that level, it’s a pretty basic statement. Of course, he’s also arguing (unsuccessfully - he wrote this in dissent and was complaining that the rest of the Court was getting it wrong) that the Court shouldn’t do that.
One thing that complicates it is this idea of “actual innocence,” which as you probably know isn’t the way the justice system usually operates. By and large we don’t deal in proof of innocence; our courts aren’t a mechanism for people to prove that they’re innocent. We either prove them guilty and punish them or we don’t and we don’t. What Scalia was saying there was that there’s no mechanism in the law for somebody who has already been convicted and sentenced to death to say “check this shit out; I was innocent all along” and get their get out of death row free card punched by a federal court because of that.
It’s essentially a statement about the way one court reviews another court’s decisions. Imagine I get accused of killing somebody, so I go to trial in Pennsylvania court. They say shit yeah, he did it, and sentence me to die. I have all kinds of appeal rights, certainly, but what’s important is that my rights to appeal are specifically defined by various statutes. Those laws tell me, and tell the courts I’m appealing to, what I can and can’t complain about and what the courts can and can’t do for me. This is so for obvious reasons - the state wants me dead in the name of Justice, and if I can effectively prolong the execution of my sentence indefinitely by constantly raising new issues and being retried all the time – what about this? OK but what about that?! - then I’m subverting Justice, right? So there are laws, and once I’ve run out of the appellate rights those laws give me, I’m out.
Scalia’s talking about one of those laws. It says “An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim—
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.”
What Scalia is saying is that if you’ve been convicted in state court, you have to satisfy the above in order for a federal court to give you any help, because federal courts stepping in and helping is supposed to be an “extraordinary remedy;” we want Justice to be administered efficiently so it can’t be a regular thing or nobody will get anything done. It is possible for you to have been convicted in state court, in a proceeding which didn’t unreasonably apply any established federal law, and also have some evidence available to you which would convince a federal court that in fact, you actually really are innocent, and in that case, he’s saying, the law does not say you get relief, because the law doesn’t say that’s what the federal court is looking for. The federal court, he’s saying, is supposed to check and see if the law is followed. Whether or not you’re “actually innocent” is a separate question based on the introduction of a bunch of facts which were already supposed to have been resolved at trial. He thinks the rest of the Court basically whizzed on the existing federal statutes in order to make up an avenue for relief that suited the case in front of them.