Nope. Not corrected. Bamboozled!
6.05(c) and 6.09(b) pertain to catching pitches that never touched the bat. Once the bat contacts the pitch, it's no longer "a pitch". It is now "a batted ball". As such, all of the rules pertaining to batted balls now apply.
If this bounced pitch goes sharply and directly from the bat to the catcher's hands and is caught, it becomes a foul tip. Strike to the batter, ball remains live and in play. If it's strike three, the batter is out and not entitled to try for first base.