An IQ test would not be given in a group setting. Maybe a CogAt or Olsat? Schools love to reference those as IQ test but they are not.
My pg ds once got a 36 or 37 percent on a vocabulary section of a standardized test. It was clearly not a good test day for him.
No child that is doing what you describe has a 75 on an ability test. It is ridiculous that the school doesn't see from what he does in school that the test is not him.
I would really look around for a tester with GT experience. Are you in a public school? You can see his records. They are not allowed to refuse that request. You can look up more information about the process online by googling FERPA. They will not show you the test itself but the full results should in there. You can get a better handle on it. If they are saying he needs Full time special education than they would be needing to do an MFE for an IEP. Are they suggesting that?
I am just brainstorming here but maybe use their suggestions against them. If they are suggesting full time special education than they should be doing a full evaluation. In doing a full evaluation they need cognitive testing done. It's part of the process. You know they are wrong about him but maybe try to make them prove it.
I have had to take the back door into getting things done for one of my kids. Feel free to pm me.
Good Luck