Although I agree there are other strategies than direct confrontation to fight bigotry, there are two aspects that go beyond your reasoning.
First, you don’t need fact based reassurance to reject any judgement not based on facts. Burden of evidence is always on those making the accusation and it’s not reasonable to accept anyone opinion unless proven wrong, because that’s how prejudice thrives.
And, related to that, people need to address their insecurities, but not at the expense of putting anyone down. As a society we can and must address the acceptance of ideas not based on facts because allowing anyone to be as hurtful as they want just because they have scars would only lead to more harm.
An eye for an eye makes the whole world blind.