I'm not really sure what distinction you're making between "reputation" and "actual historical record". When examining the military reputations of the ancient world, primary sources seem few and far between. So yes, those that are well reputed are so reputed because other people wrote about them. Or rarely, because they wrote about themselves.
The rare first hand accounts seem most suspect of them all; Julius Caesar's [ghostwritten?] Commentaries on the Gallic Wars is flagrant propaganda. PR in the truest sense possible.
On the other hand you have Scipio Africanus, who like Julius Caesar has a reputation for being one of the greatest generals ever. But anything he wrote about himself is long gone; his reputation was built by other people writing about what they think he said or did. The archeological record (the 'actual historical record'?) backs up some basic facts about the Second Punic War, but doesn't say much specifically about Scipio Africanus.
Which ancient men with lofty reputations can be said to have their reputations without "PR"?