Your explanation could also be true and at the same time feeding into the same problem if the people that have done well historically have done so because of test bias.
Your proposed experiment doesn’t test what you think it does. Since we are trying to determine if the test is biased you can’t control using the score on the test that might be biased.
Your proposed experiment doesn’t test what you think it does. Since we are trying to determine if the test is biased you can’t control using the score on the test that might be biased.