One should not confuse plausibility with authenticity; nor should we lose sight of the fact that ancient historical writing was much more about style than accuracy. Among the weapons in the historian's arsenal were set piece speeches and letters. Again the schools of rhetoric churned out hypothetical letters between contemporaries and these do occur in historical works, and collections, there are doubts about the authenticity of several of Isokrates' letters for instance and St Paul's for that matter.
The lists of works given in sources like Diogenes Laertius are equally problematic, Aristotle is credited with works that were produced by his 'school' and several well attested works are absent (Metreologika, for instance). It is thought that these catalogues derive from the book lists of the Library of Alexandria carelessly transcribed by one Hermippos who used out of date material and certainly did not check the validity of his ascriptions.
When one considers how the Library was stocked it is easy to see how exercises could be taken for authentic material. Every ship docking at Alexandria was searched for literature and it was copied at the Library and the copies returned. A manual on rhetoric would contain worked exercises of these hypothetical letters credited to various great men; a compiler then gathers a collection of a certain persons letters and includes all this cod material, a later biographer then uses the collected letters to illustrate certain points of character, et voila!
Naturally real letters did exist and some may be preserved; the ones in stone definitely are and Books XVIII to XX of Diodoros seem to preserve authentic decrees, which is not unusual if his ultimate source was Hieronymos as he is censured for his poor style, echewing speeches and dramatic set-pieces, the very things we now praise. There may still be useful matter in even the cod letters as the writer would base his exercise on something, but teasing out the genuine background from spurious accretions is a matter of pure choice (or bias) which makes the original 'facts' contained less useful and any case built on a letter fragile.
As so often it comes down to the balance of probability; how the correspondance would have been preserved and transmitted in the first place is an initial step, questions of vocabulary/syntax etc seem helpful but the preserved 'letter' may not represent a verbatim copy rather the author's paraphrase...caveat lector
When you think about, it free-choice is the only possible option.
