It might also be beneficial to have a training combatant, who is not in the same chain of command as the trainees. Gives external perspective, and reduces the chance of collusion to show "good results" if done right.
I once asked a pilot after a test mission, "if you're pretty sure they're going to do [tactic X] why don't you do [tactic that works great against tactic X]?" His response was that his mission isn't to win, it's to provide the most authentic simulation of an enemy as he can. If they don't think an enemy pilot would do something, they won't do it- even if they know they could gain an advantage using inside knowledge.
However, wouldn't the same pressures that apply to someone in a chain of command, also not apply to a contractor?
So, for example, if someone tasked with testing the current military strategy comes up with a wargame tactic that would embarrass the military (i.e. their bosses) they may not want to do that because embarrassing their bosses is probably not good for them.
However, in the same vein, someone reliant on those military bosses awarding them contracts would also not want to embarrass them, because it wouldn't be good for their ability to get contracts in the future.
In the former scenario, you at least have the case of a conscientious individual or team still going forward with what they think is the right thing to do.
In the latter there is no such compulsion either, so if anything, the chain of command argument makes things worse for contractors.