The problem with this problem is that it is bigger than just this case. Or this issue.
The problem is modernity – specifically critical thinking, as taught, to some degree or another, to almost everyone, even unconsciously by parents wanting to teach their child to encounter and discover the world around him or her. One definition I found (criticalthinking (dot)org) is the following:
“Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. In its exemplary form, it is based on universal intellectual values that transcend subject matter divisions: clarity, accuracy, precision, consistency, relevance, sound evidence, good reasons, depth, breadth, and fairness.
It entails the examination of those structures or elements of thought implicit in all reasoning: purpose, problem, or question-at-issue; assumptions; concepts; empirical grounding; reasoning leading to conclusions; implications and consequences; objections from alternative viewpoints; and frame of reference.”
As I see it, this is the way our brains are hard wired to work most effectively, and it is the default mechanism by which even the most pious of us most effectively deduce, infer, or interpret what we encounter.
It is the way, for the most part, which Rambam used to reason.
It is logical and rational, and it works. And if HKBH didn’t want us to use our brains effectively, he wouldn’t have created us this way.
The problem is that critical thinking, while it won’t necessarily lead you to question the big issues (HKBH, Torah Misinai, etc), it will undisputably lead you to recognize that people, no matter how great, are still human, and by virtue of looking at one’s own human capacities, one has to reasonably conclude that even the greatest human can err. For goodness sake, even Moshe Rabeinu did, and he was punished by HKBH for it. Lo kol shekein others?
Error in itself is not a disqualification for leadership, from the POV of anyone using critical thinking. What may be, though, is bdavka non recognition of the error, not being mekabel a better derech for the future, or not applying standards equally across the board.
It’s not for any of us to set standards for our manhigim. It is for them to set and meet standards for themselves that will not fail the test of critical thinking.