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I agree with your overall point, but technically speaking it is logically valid to prove a hypothesis false by first assuming it and then deriving a contradiction, even when the contradiction is the negation of the original hypothesis (as it is in your example).

What you should have said is that some critics start with the premise "the scientific method does not arrive at truth", and then use other people's arguments that depend on the premise "the scientific method arrives at truth" to support their claim, which is indeed logically invalid.