All of the major Roman books that we have are copies of copies of copies produced during the late Middle Ages. The oldest copies that we have date from the 1100s, and describe events nearly 1000 years earlier. How do we know that these texts aren't fabrications?
The transmission of Classical texts down to the present is a huge topic, and a fascinating one. I can't possible cover all aspects of the subject so I hope you will forgive me for this summarization.
The main way we know the works that we have are genuine is by checking them against other material. So say the oldest copy of the Martial's Epigrams is from the tenth century, but we find that a copy was listed to be in the court library of Charlemagne 200 years earlier. Writers during the period might also quote lines of these works which predate the earliest existent manuscript we have, this is very common in Byzantine works where classical Greek works are quoted and referenced by authors throughout the life of the empire which not only gives us a window into what works the authors had access to, but if the quotes differ from the material we have today, indicating changes during the copying and transmission.
A small correction would be that not all our works dare from the 11th century or later. we do have Codices dating back into Roman times themselves. Many of the oldest Codices we have are of Bibles IIRC, but not all of them. An important source for Livy is the Codex Puteanus which dates from the 5th century AD, and copies of this codex were made during the 9th century with the Carolingian renaissance.
Other sources for corroboration or or Classical texts would be palimpsests, these are works where the original ink on the parchment was scraped off, so that the valuable parchment could be reused for a new work. In more modern times, we have the ability to see the previously "erased" text. Some palimpsests were written over multiple times and can be very valuable sources of texts from antiquity or the medieval period.
Lastly we can verify the content so some classical works based on archaeology. For example Tacitus and Suetonius cover the trial of Cnaeus Calpurnius Piso, who was implicated in the death of the prince Germanicus and of attempting to illegally reassert his governorship of Syria after having left the province (if a Roman magistrate left the area over which they held imperium, they lost their imperium). Well Archaeology brought to light a bronze tablet with the Senatus Consulta on the case, which is the Roman Senatus official findings, the text of the Senatus Consulta being published at the earliest I can find being in 1996. The accounts of Tacits and Suetonius in regards to the findings and sentence of Piso and his sons conform to what is in the Senatus Consulta. This is an exceptionally example of archaeology backing up our historical sources, and many other cases aren't as dramatic but in some cases archaeology can help confirm the accuracy of classical texts.
This is just sort of a brief tip of the iceberg look at the topics, but if you want to learn more, I recommend checking out "Scribes and Scholars: A Guide to the Transmission of Greek and Latin Literature" by L. D. Reynolds & N.G. Wilson. The copy I referenced is the 4th edition copyright 2013.
For example do any books describe naval battles which divers later verified by finding shipwrecks (which the potential Renaissance forgers wouldn't know of)?