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Under what circumstances could this be the case? Come up with a hypothetical for me.
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One could have a simple and decisive proof (a reductio, let's say) that God does not exist, believe that God does not exist, but nonetheless believe that the proof doesn't settle the matter and that in fact the matter could never be settled.
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Something cannot be grounded in fact yet fall short of the justification for knowledge. Sure, something can be grounded in a demonstration of reality and fall short of knowledge. (A guy in a ski mask with a gun in his hand standing over my dead wife with a gun shot wound is guilty through evident demonstration of reality. It falls short of knowledge because he could always wear a ski mask due to light sensitivity and that he walked in on the scene and picked up the gun out of stupid curiosity.)
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Semantics. The point was merely that the belief could be very much informed by the facts, in contrast to your previous claim:
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then atheism cannot be based on knowledge and must be a belief held completely irrespective of the facts and of reality.
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Surely the belief that the masked, armed man standing over the corpse is the killer is not a belief that's "held completely irrespective of the facts and of reality", yet this would be an example of such a scenario where one could have a reasonable belief that isn't an instance of knowledge.
