Six Iraqis were asking the court to order an independent public inquiry into allegations that soldiers may have killed up to 20 captives held after a gun battle in southern Iraq in 2004.
They are putting medical evidence before the court which they say supports their contentions that captives were tortured, murdered and their bodies mutilated.
By publishing the legal advice that his predecessor used to justify the techniques, yet making it clear that he does not intend to press charges against those involved in the decision-making or the interrogations, he has left himself open to criticism from the right and the left.
Some of the strongest comments have come from his own supporters, who believe that the president can not simply wipe the slate clean; that his call for "reflection, not retribution", amounts to a whitewash.
There are plenty of voices calling for a full investigation, with charges being pressed against anyone found to have committed acts of torture in the name of the United States.