It's easy to pick holes in a massive retcon but when re-watching earlier episodes a few things do seem to support it and it explains his arrogance in earlier seasons.
BASHIR: Captain of the team at Starfleet Medical Academy. We took the sector championships in my final year.
O'BRIEN: Against other medical students?
BASHIR: Against everybody. Played a Vulcan in the finals. Talk about stamina. I don't think he ever actually broke a sweat.
O'BRIEN: And you won?
BASHIR: Took him on a back wall riser shot.
3x18 "Distant Voices"
ALTOVAR: Remember, Doctor, I'm inside your head. I know all about you. When you were younger, you wanted to be a tennis player, didn't you.
BASHIR: I wasn't good enough to play professionally.
ALTOVAR: Don't lie to me. Not in here. You were good enough. But you knew your parents wouldn't approve of it. So you gave up and you became a doctor instead.
BASHIR: I love medicine.
ALTOVAR: But you loved tennis more. And what about medical school? You should've been first in your class. What went wrong?
BASHIR: I made a mistake in the final exam.
ALTOVAR: You mistook a pre-ganglionic fibre for a post-ganglionic nerve.
BASHIR: That's right.
ALTOVAR: But pre-ganglionic fibres and post-ganglionic nerves aren't anything alike. Any first year medical student could tell them apart. You purposely answered the question wrong.
4x24 "The Quickening"
BASHIR: I'm going to tell you a little secret, Jadzia. I was looking forward to tomorrow, to seeing Kira again and casually asking, how was the nebula? And oh, by the way, I cured that Blight thing those people had.
DAX: It's not a crime to believe in yourself, Julian.
BASHIR: These people believed in me and look where it got them. Trevean was right. There is no cure. The Dominion made sure of that. But I was so arrogant I thought I could find one in a week.
DAX: Maybe it was arrogant to think that. But it's even more arrogant to think there isn't a cure just because you couldn't find it.