seems to me if it's backed up to your line then the water doing the mess is yours. Is the main line plugged or just surface water doing the damage. Install enough standpipes and terraces to stop your water or slow it down. really no problem to you as it seems you have enough drainage and fall.. cut the main off at the property line and let it run on the surface. They decide to fix it they can tie back on.  few load of stone on the property line to stop erosion.