Right you are about precincts v. counties, but don't you mean precincts are more a 'fine' gradation rather than 'coarse'?
See post #124.
The breakdown of voting districts into finer gradations (yes precinct is finer than county in that sense) leads to more coarse data in smaller groups. The 'proportional assignment' is more coarse (= less smooth, less averaged, more raw) at the precinct level than at the county level.
Semantics aside (and the above are the proper statistical semantics) the issue comes to accuracy and what constitutes 'illegal' or improper ballot.