The story's a writer's conclusion, not a smoking gun. Obama could have doomed them just by staying unavailable or not giving the available reaction forces a 'Go' order, I'm thinking there is a pretty good chance there will never be a real Obama order to stand down unearthed.
Thing about the US military is that despite all the bullshit they teach about how great our tactical flexibility is once we have a mission order, that's a lot less true than it used to be, and these days it hardly exists above the battalion level, and often not even there. The Army and DoD generally love control a whole lot more than they love actual results, if there is any risk at all involved in achieving said results. This fundamental flaw has only been made worse by rapid global communications.