I think that would depend on who is responsible for the litter left over after mowing. If it is just left there or if the plot owner is responsible, then perhaps the father/reverend has a point. I doubt the cemetery itself would hold itself responsible for cleaning up messes from unsuitable items being left on the gravesite on mowing day.
In this case, the cemetery had grave markers flush with the ground so that the mowers could just drive over them like any other lawn. The cemetery workers would have had to remove all of the flowers from the flower pots embedded in the grave markers before mowing was done. The workers cemetery would also have had to pick up "Winchester's" box planter at the same time with no problem.
The dark hearted Preacher without doubt only wanted vengeance against Winchester for causing the alienation of his daughter. A small petty man with a chip on his shoulder.
You will respect my authoritah!