Suspicions will be initially aroused if claims lack substantiation. A request for substantiation is reasonable, but often the response is not. Unreasonable responses run the gamut from appeal to revelation (for deities) through conspiracy theory (for secret knowledge), pseudo-science (for nutritional supplements, young-earth creationism, infallible diets, the list goes on...), to legal action (for, amongst other things, alternative medicine).
"How do you know?" If we ask this question when presented with claims for, say, effective treatment for cancer, here are two possible responses (there may be others, but these are the important ones — the ones that tell us most about the motives of the responder).
Response 1: "We did tests. Here are the results. Judge for yourself."
Response 2: "Shut up, or we'll set the lawyers on you."
The Clinic's response: "Shut up, or we'll set the lawyers on you." It speaks volumes.