Absolutely! Anyone who has worked in that environment (either totally or on the fringe) knows this to be fact. Plausible dependability. My guess is the public statements that Obama said he told his advisor’s was never in writing. Also, everything Obama says verbally must be restated by his minions, because what he says and what it means, is always restated.
If he issued no order, he left the military in the lurch, which, (I think), would be the same as a stand down order.