I'm pretty sure the Hobbs (certainly in the planes I hire) only turns over when the oil pressure reacehs a certain level. I.e. when the engine is running. At this point you are most certainly in command of the aircraft and hence should log (and pay) as such.
I can't see how you can pay for a lower time than you log. Surely you can't say that taxiing is not logged time?
Hence you should pay for it as such. If I could get away for only paying for the time above a certain airspeed I'd have a lot more hours in my log book and have saved a fortune! Most of it would have been spent taxiing around the airport though rather than boring holes in the sky.
Cheers,
R.