If a basic statement and theory are incoherent, then observation reports cannot inform us that theories are wrong and theories cannot inform us that observation reports are wrong. Either the theories or observation reports are wrong — or both. Neither T1 nor T2 should be adopted a priori, for they effectively annihilate one another: all we can see is an incoherence between T1 and T2.
Furthermore, even after we recognize an incoherence between an observation report and a theory, this ‘recognizing’ is relative to a given system of logic, background assumptions, language, and cognitive framework: we are even fallible in recognizing incoherence. Whatever method or route we follow that leads to preferring one over the other will either not rest on an Archimedean point, or will not be known to rest on an Archimedean point. All is theory-laden and subject to error. We must admit that it is possible to change the logic we employ, statements we adopt, theories we accept, methods we follow, language we use, or the cognitive frameworks we inhabit, for none of them are privileged.