Order of reaction for hydrogen ions being ignored
Imagine you are doing a process which takes 'n' steps. Label the steps : 1,2,3..n, now consider the time it takes to do step 1 , step -2 and so on. Now, wouldn't you agree that the time taken to complete process would be entirely dependent on the step which takes the most time(slowest step) to complete?
So, in your example the hydrogen ions are in one of the faster steps. So, if the concentration of hydrogen is 'enough' such that once you come to the step that their ample hydrogens to fuel the reaction, then it would seem that rate is independent of hydrogen concentration ( I say seem because there may be minute effects of it on the rate)