I think you missed the point(although you're talking about something else valid. It's not the actual boundaries and who's in each one, for the pure maths discussion in this case. It's that the boundaries are in anyway judged be population. If boundaries were purely done on geographical size i.e. every 10 km2, then Benfords law would apply, as population sizes would be randomly distributed amongst them. But they're not, they're designed to have roughly the same size of population.
The population sizes are still randomly distributed in the politically manipulated precinct boundaries. They will form a bell shape curve which is roughly symmetrical around the mean. The problem with the maths is that the bell shaped curve is squashed into too narrow a range on the x axis. So not exactly to do with randomness, and more to do with variance.