You're talking about accuracy. A text is authentic if its origins match those that are attributed to it; i.e. a 4th century letter that was actually written in the 300s C.E. is authentic regardless of whether or not the content accurately records any events that happen during that time period. Inauthentic documents are usually later copies with interpolated material, glosses, outright forgeries, false documents, etc.

The issue of accuracy is one of the problems of historical evidence: every writer has biases, every document is written for a specific purpose which can color its account, and none of them are perfect. Documents from closer in time and geography to the actual events, especially by someone in a position to have first-hand knowledge of said events, are generally more valuable than those from later authors because there is less time and distant to distort accounts - but every account has to be balanced against whatever other historical (and sometimes physical or archaeological) evidence we can find to try and reconstruct what happened at a given point in time.

False accounts, those which seek to deliberately misrepresent events, can sometimes be very difficult to suss out, especially if they are very old (and thus have a large body of secondary & supporting literature) or if there are few other accounts to conflict with it. More common are inaccuracies and honest mistakes, the kind of variance in witness testimony that the film Rashōmon is based on - and these can form the basis of some considerable historical debates.

A very good book on this, if you want to dig deeper, is The Historian As Detective: Essays On Evidence.