[xracy]

The wider claim doesn't actually change anything about the discourse. You have not contributed to the discussion, because you've provided no additional information about whether or not the underlying claim is true. We are no closer to truth because of your comment. So you have not "dispelled the mistaken belief that stereotypes are mostly false in general" because we can't make an active assumption about this stereotype without directly proving it.

So... Their original point stands without direct evidence against it. As you have not provided direct evidence, your point is moot.