It's not just a "warped sense of trust for science." There's an extraordinary amount of self-delusion and denial of near-infinite evidence that goes on in this belief. Literally that every single space agency is a giant conspiracy to make everyone believe that the world is a globe. That gravity is a fake conspiracy orchestrated by millions and millions of people. That engineering simply does not work and has never gotten us into space. That satellites don't exist and that the ISS is a soundstage or cgi or something. That the sun is 5 miles in diameter and goes in a big circle on top of a flat disc earth, and that by some miracle it makes a perfect illusion of us rotating around when in "reality," we're perfectly still in the centre of the universe. That all the stars rotate around us, and that earth is the only planet that's flat out of trillions and trillions because "reasons." I could go on and on and on and on.
This is not a warped sense of science. Having a warped sense of science is thinking that alternative medicine works. This is dozens of levels above that.
Yes but even a scientist has to be pretty arrogant to say "this is fact and we can prove it" because in reality everything you're testing and proving is only possible within a certain set of conditions ie, dimensions, physics laws, etc. However, these laws are only applicable in our visible universe. There's always the possibility that outside of these limits there are different rules.
Sorry if im not explaining it right. Just think of our science stuff as drawings on a paper. Everything that we do and test only works on the sheet of paper we exist in, so to assume that these apply to everything else makes you automatically incorrect. Our earth may appear round and we can simulate and test that its round, but in the end we'll never know if it is actually round. It could be square and light just warps it to be round. Our simulations could be all incorrect because after a certain size molecules yield different results.
Theres infinite possibilities for stuff to go wrong. These people who believe in the earth being flat are neither wrong or right. They're just believers. Of course, they have much less credibility than everyone else.