I'm guessing that the rules prohibit using some of the pedal power to charge a battery during the initial part of the run, and then using that stored energy to provide an additional speed boost :D
I don't see why not. The initial run is essentially the storing up of momentum. From that, running up a flywheel inside the bike is just storing the same energy in a different place.
It stretches the concept of "human powered". Why not just pedal while stationary to charge a battery (take as long as you like), and then ride the course with no additional expenditure of effort.
Because then you would be bringing additional stored energy into the competition (beyond what's in your body)?
Well, the course is a 5mile run up to a 200m speed trap. So if you allow batteries/motors, you could just sit stationary somewhere in that 5 miles pedalling for a while, and then use electrical acceleration to get up to speed for the trap. You're not bringing any additional energy, but its clearly not in the spirit of the challenge.