The other way to look at it would be:
The narrator is describing what Mihawk is regarded as in the OP world. Mihawk's status in the OP world is the World's Greatest Swordsman. Roger's was the pirate king, hence narrator called him the Pirate King. Rayleigh regarded as the Dark King, hence called the Dark King. The narrator simply describes what they're regarded as within the world of one piece.
But then that means at the end of the series, when the narrator calls Zoro the strongest swordsman, there's again no actual reason to believe him then right?
Like even if Zoro beats a guy stronger than mihawk, theres no actual proof that that guy was the strongest, and if Zoro beats a guy even stronger than that, there's again No proof that even that guy was the strongest.
Like even if Zoro beats the strongest swordsman we actually ever see in the series, we know random strong people exist in the world such as Fujitora and greenbull so once again, Some off screen guy could still be stronger than Zoro.
See how that goes?