What it plainly implies in the present case is that the actions of Maj. Nidal Malik Hasan should not be assumed in any meaningful way to be related to his Muslim faith.
Perfect subjective knowledge of the major's possibly disordered mind is not available to me, but nor is it available to the host of damage-control commentators and FBI drones who have had things mostly their own way so far. In order to demonstrate the absence of a connection, however, the following facts would have to be regarded as relatively random or secondary:
1) Hasan had been in direct correspondence with a notorious preacher of violence, Anwar al-Awlaki, whose enthusiasm for the teachings and actions of al-Qaida has long been well-known to researchers and intelligence agencies.
2) He bought weapons for himself well in advance of a murderous assault on unarmed soldiers awaiting treatment at a clinic—people to whom, in addition to his responsibilities as a human being, he also owed, as a physician, a sworn duty of care.