Discounting a conspiracy as impossible is just as silly as arguing a conspiracy of hundreds. Improbable, yes, impossible, no.
No, because the people at the top are not the ones who do the work. They set policy, and sometimes directly tell people what to do - but, more often, they tell people who then tell other people what to do. If a conspiracy is going to involve the top of the chain - and it should be pointed out that the VP is technically not in the chain of command - then it's going to involved dozens, if not hundreds of others if the conspiracy is actually going to do something effective. And in that case, there will be enough written down that eventually it will out. See, for example, the Iran-Contra affair.
An excellent account of both what the critical points for intervention were, and what happened on the day is "The Ground Truth": http://www.amazon.com/Ground-Truth-Untold-America-Attack/dp/... The title has unfortunate "truther" connotations, but it comes from a term the aviation industry uses to establish what happened after a crash. They use first-hand material and evidence to establish the "ground truth" of the crash, and from there try to extract lessons. The author does exactly that, using primary sources exclusively - such as recorded conversations between air controllers - to determine the sequence of events.
In either case discounting a conspiracy as impossible isn't silly if there's no evidence of said conspiracy nor even a plausible hypothesis of how such a conspiracy could have worked. The onus of proof is on those proposing a conspiracy, not on everyone else to prove a conspiracy didn't occur.