forum 8: week of 5 March: tests and evidence
What you call the "simple statement" is not so simple for the following reasons: (1) the scientific/experimental setting is evidently different from the traditional epistemological/philosophical setting; (2) defining accessibility in the various contexts is not quite as simple as you would (like to) think due to the nontrivial differences between the scientific/experimental setting and the traditional philosophical setting. Putting those two reasons together, justification and accessibility are key concepts that have not been paid much attention to in science, and appropriate definitions of those key concepts really need to be spelled out in detail in order for us to make any sense of those differences in my first reason (1).
You say, "If I cannot logically and consistently set out my evidence then I don't actually have an argument at all, right?" My response is: The big problem that still exists today is that it's not generally agreed upon what counts as "good" evidence vs. "bad" evidence! This lack of agreement could play a role in what the requirements are to have an argument! Hence, once again, it does not seem quite as simple (in my opinion) as you think it is.