It is possible that the host exaggerated the facts, as this is a common tactic to capture attention, but these two swordsmen certainly possessed a certain level of fame.
Genji Shiru goes without saying; he was known as one of the Seven-Pointed Star, so naturally, he had his unique strengths.
As for his opponent, "Ghost Subduer" Stern, he was said to be the first swordsman from Breakthrough to reach the summit of Sword Mountain.
Chapter 315