What we know about Ancient Greece comes from a range of different sources, both literary and material. We are most certain about things when they are corroborated by various sources. We know Thucydides didn't make up the Athenian Empire because there are inscriptions listing the tribute owed by its subjects; we know the Athenians built the Parthenon because it's standing right there on the akropolis. We know Sokrates was a philosopher because no fewer than 3 contemporary authors wrote about his ideas at length.

That said, ancient historians must always be careful about what they presume to know. We do not have the kind of comprehensive documentation that allows modern historians to verify eyewitness accounts or gather statistical data. The surviving literary material needs to be read critically, because it never just tells you the facts; every work is shaped by its author's personal experience, his biases, his aims, the genre in which he was writing, and so on. Our understanding of the sources is further reduced by our imperfect knowledge of their nature and context. We don't always know why or for whom a source was written; we aren't always sure we grasp the niceties of its language or its tone; we can't always figure out what a missing piece of a text is supposed to have said. In short, there may be some things we know quite well, but there are also a lot of things we really don't know at all.

Anecdotes about famous figures like Diogenes, gathered by an ancient source, are a case in point. On the one hand, a lot of these anecdotes seem fantastical and exaggerated; they clearly arose from a desire among learned elites to caricature a known figure and dial the things that made him famous up to eleven. On the other hand, this is all we know. How are we to separate fact from fiction?

In the case of tall tales like these, the choice is really with the historian. Some may be inclined to take them at face value, reluctant to just throw out anything that might tell us more about the ancient world; others will present such stories using words like "allegedly" and "it is said" (as the ancients actually often did themselves), acknowledging that there is really no way to know for sure.