It seems pretty simple. No matter what, nobody can possibly know how all those ancient concepts got invented unless they could actually go back in time and check, all of you are making assumptions, which can never be taken for fact.
We do however know what the scientific method has achieved, because it has been documented.
The best you can wring out of this one is we don't know what the Zetetic method, Mysticism or Superstition are responsible for. Logic implies that it is accidents and experiments that achieved those things, but we cannot know for sure, so it's a null matter.
We do however know what the scientific method has achieved for humanity through time, and it has time and again been proven to work.
I'll take it as a concession of defeat from the FEr's if they fail to come up with a logical, step by step explanation of why the scientific method does not work well enough for them to validate the FET.