Am not sure the second part is always true: there might be situations where statistical approaches could be made kind of "infinitely" accurate as far as data is

Am not sure the second part is always true: there might be situations where statistical approaches could be made kind of "infinitely" accurate as far as data is concerned but still represent a complete misunderstanding of the actual situation (aka truth), e.g., layering epicycles on epicycles in a geocentric model of the solar systems. Some data might support a statistical approach other might not even though it might not contain misrepresentations as such.