I don't know the truth of this, but one of the (plausible) explanations I've heard so far was the fact that everyone -- including the shooter-- was in uniform, in a densely crowded place where surprisingly few are actually routinely armed except the MPs and civilian cops. The shooter could have simple taken advantage of the confusion in some densely crowded spaces. After the initial confusion, how unusual would it have been to see another armed man in uniform running down a hall with a sidearm drawn? So, is that the shooter, or someone looking for the shooter? How would anyone freshly on the scene know?
So, even if the MPs responded fast, it could still take them some time to figure out who/where the shooter was.
Though, if other reports are true, then you'd think the first assumption would be "the guy screaming Allah Akhbar and firing off rounds at troops." But, we weren't there. Surely, there were folks there who saw the shooter and who were certain, but not until that was also an armed someone who saw the shooter and was certain was anyone in any position to effectively do anything to stop him -- and, apparently, that civilian woman cop and her partner did just that, when they were certain--but until that time, the shooter was able to take advantage of a lot of confusion in a crowded place. The confusion was understandable, if everyone is wearing the same or similar uniform, and also has a plausible expectation of seeing other armed personnel in uniform with weapons drawn in that situation. I don't envy the responsibility of those who had to make quick decisions, friend or foe, under those circumstances, nor would I second guess them. "Kill them all, and let God sort them out" thankfully wasn't the option that the authorities chose.
Is there any substantial difference between "a wigged out nut" and "a wigged out terrorist nut?" As tragic as this incident is, 300 million other people did no such thing that day. This was 6-sigma fringe lunacy, terrorist or pushed over the edge unstable guy, hardly makes a difference. If it was part of some widespread deep seated terrorist plot that is taking decades to unfold, then it is a widespread deepseated plot that so far is a way far distant second to highway mayhem, which never makes it past P8 of the local paper.
We kill more of each other rushing home from the really, really good Italian Ice on the other side of town and so on(ie, for no compelling reason whatsoever other than our freedom to do so) than every terrorist organization in existence.
The aspect of this I find intriguing is, we have a 'volunteer army.' He seems like he accepted the medical training, and the degree, and a career in the military, and all of that, but ... yes, but...clung to his personal politics. Clearly a bit too hard. OTOH, the whole point of having all those folks in uniform is to insure precisely our right to do that.
Six-sigma fringe lunacy, that's what it seems like so far.