It's not exactly that the rules contradict themselves.
It's just that the whole 'pass the bomb' situation can result in opposing players fumbling a pass in the active players turn. Now if this did happen without that wording then it would be a turnover regardless because the rule for fumbles doesn't actually care who fumbles the ball (Dump Off has a similar exclusion to avoid this.)
I think there just needs to be clarifying text that makes it clear that "A turnover occurs if the bomb detonation knocks over a player on the active team." And a little reorganising so that the text about fumbled bombs mentions that they detonate right afterwards.
A quick try here: I've italicised my changes and broken the text apart just for ease of reading.
Bombardier (Extraordinary)
A coach may choose to have a Bombardier who is not Prone or Stunned throw a bomb instead of taking any other Action with the player. This does not use the team's Pass Action for the turn.
The bomb is thrown using the rules for throwing the ball (including weather effects), except that the player may not move or stand up before throwing it (he needs time to light the fuse!). (Is stand up needed here? As the first sentence already excludes prone players from trying to throw a bomb)
Intercepted bomb passes and fumbles do not cause turnovers, but a player from the moving team being Knocked Down by the bomb detonating will. (See Turnover Rules on page 8.)
All skills that may be used when a ball is thrown may be used when throwing a bomb.
A bomb may be intercepted or caught using the same rules for catching the ball, in which case the player catching it must throw it again immediately. This is a special bonus (Pass?) Action that takes place out of the normal sequence of play.
A player holding the ball can catch or intercept and throw a bomb.
The bomb explodes when it lands in an empty square or an opportunity to catch the bomb fails or is declined (i.e., bombs don’t ‘bounce’). If a bomb lands in the crowd, it explodes with no effect. If the bomb is fumbled it explodes in the bomb thrower’s square. (Slight reordering to allow flowing straight to the detonation rules from the fumble)
When the bomb finally does explode any player in the same square is Knocked Down, and players in adjacent squares are Knocked Down on a roll of 4+.
Players can be hit by a bomb and treated as Knocked Down even if they are already Prone or Stunned.
Make Armour and Injury rolls for any players Knocked Down by the bomb. If a player from the moving team is Knocked Down by this, it will cause a Turnover.
Casualties caused by a bomb do not count for Star Player points.
I'm sure it can be cleaned further, but how's that for starters?