How is it flawed? I am presented with a claim that "there is a God".
Why is it flawed to then test that claim?
Then forget science. Talk about the jury verdict. It is the same thing. They are testing against the null hypothesis of "not guilty". That is the essence of our judicial system. Why is it not allowable to apply it to other claims? You surely can't believe juries make most of their verdicts on numerical data. It is the same reasoning, the same rubric, however.
You disallow that one may use scientific reasoning to draw a conclusion, now you seem to be denying the use of any reasoning to come to a conclusion.
I am curious how you test claims in your life. Or are you literally agnostic about any and every claim presented to you?