I pee in the shower, so not all grey water is created equal. ;)
With that said, I have dumped grey water onto the ground twice, and both times it was during periods of huge rain, an inch or more per hour.
Also, both times, there wasn't someone coming to use that site the next day, as I was staying on that site the next few days. No big deal and I didn't notice any smell when the rain finally stopped.
To this day, even with a restroom, I pee in the woods, and when we tent camped, I peed and pooped in the woods, and washed dishes at the campsite. I have fixed breakfast for 20 campers and then washed the dishes at the campsite, dumping the waste water onto the ground. Breakfast for 20 people creates a lot more than one small tub of grey water. Somehow, none of those tent campers got sick. :R