Neither example is meant to be implied as the only possible way of for forming that kind of distrust rather examples of logic used and types of conclusions reached. I could just have easily said "people who think lizard people want to hold us back from discovering advanced math" as a reason some deeply distrust all formal math and your response would be focusing on how there are other ways (besides lizard people) to deeply distrust all existing math - completely sidestepping the actual point point around the absurdity and unfalsifiability of the type of conclusion about deep distrust of all of math itself vs the types of conclusions normal distrust reaches (e.g. "I know not everything in a maths textbook will always be right but I can try to think about each consideration independent of a central conspiracy on all of math".
Put another way without specific example or analogy: if there is some organization as large as a nation's government (thousands upon thousands of organizations, possibly millions of people) and you can't weigh things done by said government without always invoking a single nefarious/secretive plot or group being behind it every time then you've left the realm of standard or reasonable distrust and entered the realm of unfalsifiable, unhinged thinking the article is meaning by deep distrust. Even the worst governments in our world's history aren't reasonably measured that way. The alternative to this is not blind trust, it's normal distrust GP was arguing for.