Does this then mean that we can be reasonably certain that people or beings named Herakles, Homer, Zeus, Isis, Chalchiuhtlicue, Ganesh, Vishnu, and Yen-Lo-Wang all existed too? If merely being mentioned in ancient texts qualifies one for certainly having existed, well then, we have a crowded hall of deities to explore.
On the other hand, if you have several ancient folks, and you have more than one text naming all of them, or some of them, you probably have much less of a problem.
Most of these debates center on Biblical references, although you see the same arguments popping up with regard to Sumerian texts. The Chinese burned most of their stuff from time to time so there's less conflict.
Still, if I were to suggest that you don't exist because none of your ancestors 20 generations ago was ever mentioned in any records, you would respond that my analysis was faulty. That's why I have confidence that you can be brought around to understanding the concept of "preponderance of evidence" even if it should be one reference made 3000 years ago.
I think that's the phrase you are grasping for and not finding ~ "Honest Abe" and "Young George Washington" are certainly as much creations of literary license as they are their mothers' loins yet we do not doubt they existed.