Actually that hearing is in regards to a Writ of Certori filed in 2009 in regards to Burnett's ruling on the DNA claim.
The Defense is essentially asking the ASSC to review Burnett's ruling for procedural errors.
The ASSC can't grant a new trial over the hearing - they can't even rule on the DNA claim itself, as it's still in the circuit court's jurisdiction.
They can only order Burnett to rule again on the DNA claim if they find he did in fact err.
Echol's only remaining "appeal" is the federal Habeas Corpus writ which was filed in 2007.
In that appeal, Roirdan attempted a "Schlup/House" claim in order to use the DNA testing to enter other evidence that normally wouldn't have been allowed in Federal court.
That claim has been held in abeyance until the DNA claim was exausted in state court, and once it is, it's no longer a valid federal claim - and the HC writ becomes meaningless.
That's why the Defense is dragging the state exaustion out as long as they possibly can.
