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On one hand you have theories that can be distingished by evidence. On the other you have theories that cannot be distingished by evidence.

Do you have any evidence that you can extrapolate from one to the other?

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The No Supernatural Explanations theory applies on the face of it to the god/no god pair of theories. The point of theory making in general is to extrapolate, even to situations that are counterfactual and thus can never be directly tested. You could ask on what basis is any theory generalized from data... what evidence do you have that the new data will obey the same rules as the old? At some point an inductive bias is needed. I will grant you that.