You have this wrong. A "habeas court" is a court considering whether a person is being detained illegally. This is a mechanism for obtaining a collateral review of evidence in a criminal case (commonly used in death cases), since a person can't be legally detained or executed if they didn't commit a crime.
In the Scalia quotation, he was using his lawful-evil dissent persona to cast aspersions on a very common review mechanism. This was his much regarded "style," but it doesn't really help people understand the state of play in this situation.
You fall into the trap. Unlike the golf commissioner (if they even regulate golf in OK counties), the habeas court is actually sitting in the center of its constitutive authority when making decisions on actual innocence in capital habeas.