Washer water goes in to black tank.

For me it just does not make sense to route the washer drain into the black tank, exactly for the reason you encountered. Ours goes to the grey tank. And I leave the grey tank valve open when camped unless I need to build up some volume prior to draining the black tank. At least if I forget and leave the grey tank valve closed and run the washer, the worst that will happen is grey water will back up in the shower rather than black water up thru the toilet or toilet vent.

Probably just easier and cheaper for them to route it to the black tank in your case.