Exams are the formal yardstick here, and a serious institution should not subject itself to such a powerful and informal system that is completely unchallengeable and opaque as "your supervisor's secret opinion of you".

If "stupid people" are passing these exams, maybe these are not good exams either.

Finally, thinking in terms of "stupid people" also incorrectly frames intelligence as a scalar, is unhelpful and lacks descriptive power of how one's mental capacity falls short: Are they socially clueless? Are they forgetful? Are they not able to put in the mental work when it comes to answering questions?

But intervening on a test result makes you look suspicious and opens you to narrative about motivation.