Some people have suggested that they drew their conclusions from a sort of positivist view, which is the philosophical basis of classical pluralism. Basically, it says that the senses are the only source of knowledge, and that no unobservable entities exist (or that they can be counted on beyond a reasonable doubt). While my understanding of this paradigm has always been in the political science realm, it is used in observing scientific phenomenon, or it least it was centuries ago.
The issue is that much of modern science operates with the understanding that many things can only be proven to a theoretical "highly probable" level. This I would argue is the conventionalist view. Nobody but the irrational or the ignorant doubt that cell theory (for the most part) is true, but it can never be "law" because there are holes in the system. Likewise, relativity and space-time are rather unusual concepts, but simplify our understanding of other scientific phenomenon. Gravitons don't really exist ad physical particles but assist us in our understanding of gravity.
The point is, positivism is good for understanding some things, but it cannot be the only approach we take. The positivist flat earthers argue that we can only make conclusions based on empirical observation. Because many of them have not flown internationally or been in space ships, they attribute an infinitely greater likelihood to FET than to RET. When they look out their windows they see a flat earth, and reach their conclusions on the shape of the Earth based on this simple observation.
The problem I see is not in their conclusion, but the method by which they
reach their conclusion
EDIT: for more refer to the following:
http://en.wikipedia.org/wiki/Karl_Popper#Philosophy_of_ScienceWe've been reading a lot of this in my "theories of political research" class. I hope that some people find it enlightening.