You should read about "the arbitrary" in OPAR.
First, you write "A casual inference, relying on the claim that there are casual structures, makes it very low probability that the farmer has not produced a green bowlingball-size sallad since there has not been any rain at all and other farmers have seen their fields turn into dry deserts. There are not enough ingredients for such a phenomenon to be produced." But the evidence you provide is actually enough to justify a probability of zero, not just "very low."
Second, the claim "that you can't trust that there are reliable casual relationships in the world" is a claim that reasoning as such is impossible. As Peikoff puts it, "reason cannot be neutral in regard to such a claim." So that claim should be dismissed.
I would therefore conclude that the eleven people are lying.
Epistem reacted to necrovore in Justification: Casual inference vs witness testimony