BTW - he is in a Private "school for gifted" and grade skipped and they are saying that he wouldn't qualify for a grade appropriate GATE program at a public school.
Of course, it is in their interests to say this, if they think that a consequence may be that you leave him where he is and so they continue to get fees for him. I'm not saying they are falsifying the test results, of course; that's most unlikely. However, (a) they do have an incentive to be rigid about not looking for a way round this problem (b) it would be naive of the state GATE programme to accept *only* recommendation from current school as a way in, because of the conflict of interests. So I would think that talking to a human being at the GATE programme, other test results in hand, might be a good thing to do (in addition to asking the current school what on earth happened in this test).