Thanks John, that I what I always thought but someone recently told me that the water goes straight to the main drain.
Never heard of a "main drain" on a 5th wheel trailer. If by main, they mean the one for the black tank, think about it. The washer can use up to 11 gallons or so of water for a cycle. That would certainly fill up the black tank faster than most would appreciate. The shower and lavatory sink use a lot less water than the toilet does over time. But the drain from the tank valve does connect to the same sewer drain outlet that the black and galley tanks do, so maybe that's what they meant by "main.".
On a side note, when we used our washer, I typically opened the valve for the bathroom gray tank, just to be sure it didn't overfill if I hadn't dumped all tanks in a while.