Your statement that the odds of getting injured don't change with experience assumes that each time you run the rapid is an independent event. Like flipping a coin.

That is clearly not the case.  Each time you run a rapid definately has influence on the subsequent times you run that same rapid.  And to a lesser degree there is an impact on the probablility of getting injured in other rapids as well.

Each time you run the rapid, you gain a certain amount of experience that will affect your judgement on how best to run that rapid.  This can manifest itself as gaining skill to more effectively run the rapid, but it could also have other effects such as developing a psychological barrier to running the rapid well.  Or in the extreme case, developing the judgement not to run the rapid at all, in some case cause you to quit boating all together.  

It's difficult to predict the probability distribution of danger as experience increases, but we can say with certainty that that distribution is not uniform.

-Just My Opinion, Otter

PS: Glad EJ made it out all right.