General Wilkinson, the military commander in New Orleans. He blocked the delivery of Swartwout's writ from the territorial judge, then transfered Swartwout as a prisoner beyond the judge's jurisdiction. The Supreme Court ruled that Swartwout and Bollman had a right to this writ because its suspension was not constitutionally enacted. It is actually a very similar case to the 2004 Gitmo ruling, where the court found that habeas corpus had not been constitutionally suspended even though it was being denied.
I think you need to go read up on the case a little more. General Wilkinson did not suspend habeas corpus, nobody did. He claimed the Supreme Court didn't have the power to issue the writ, and Chief Justice Marshall set him straight. But as a sidelight to that, since neither Congress or the President had suspended habeas corpus then the Court was not in a position to rule on just who may suspend it.
Nice try though.