"But you can't prove it's impossible for my mind to spontaneously generate a belief that happens to be correct!"

Whether the belief happens to be true is irrelevant. What matters is whether the person can justify the belief. If the conviction is spontaneously generated, the person doesn't have a rational argument that shows how the claim arises from previously-accepted statements. Thus, asserting that claim is wrong, regardless of whether it happens to be true or not.

It's not about truth! It's about justification!