This is a very valid question and the answer, traditionally, is that the historian uses their judgement in combination with logic and collateral information to evaluate claims.
First of all, many historians make no claim as to the authenticity of the information they are reporting, they just report it. For example, Herodotus will just say "so-and-so told me thus and such". Sometimes he will say "I found this unbelievable because..." and then give his reasons.
Many historians do not even do this, they just accept what they read and repeat it uncritically. For this reason you can find the same mistake being repeated over and over in many books. For example, the main source of information on the American Revolution is the book Storia della guerra dell' Independenza d'America (1809) by the Italian Carlo Botta. This book was translated into English and widely used by American historians to "document" the American revolution, even though Botta did not speak good English and had never even been to America. Consequently, American history books are loaded with incorrect or garbled information that Botta either made up or exaggerated.
To answer your question more specifically, a historian can infer what happened by using logic and collateral information. For example, you will see the claim sometimes that the Soviets colonized Prussia with Russians after they conquered it in World War II, but if you actually go to Kaliningrad, formerly known as Konigsberg, you will find many Poles there, and they are in fact by far the dominant group. From this you could infer that a systematic effort was made to introduce Poles into conquered Prussia, even if you did not know this from documentary evidence. You can use collateral evidence to infer what must have happened, even if it is undocumented or documented incorrectly.