That's good he wants to accelerate.
Unfortunately I don't have any other ideas about getting around their "proof" except having your son prove them wrong.
I would be more specific and instead of explaining it in terms of ALL tests, I'd explain why he needs to focus on the timed tests. I wouldn't make a big deal about the grade. Instead I'd say, "I'd like to help you get more challenging math. One of the problems is that you're not putting in enough effort on the timed tests. I can understand your frustration, but if you put more effort into the timed tests, it would help in getting you accelerated in math."
If that won't work hopefully someone else will have a better suggestion for getting around their "proof." My DD's the same way with those kind of tests, so I'm interested in hearing other ideas! Thanks for bringing it up.