There is a very easy solution to this.
It's a water bottle. Birds are so smart it's easy to do! If a hamster can learn, surely a parrot can. We all know parrots are smarter than hamsters!
Both my girls are water bottle trained. I started them with cheap green plastic ones from the petstore, hung them near the water bowl and showed them how they worked. Within days they had it down. Now I use glass Snapple bottles and the lixit 'beverage bottle' kit. They're much better quality and if I break a bottle, I just get a new one.
You still should change them daily (I do it every couple days, as I'm a horrible Mommy). You should also check them to make sure they are functioning daily, especially if they were food dunkers. I switch them about as often as I run the dishwasher. I have one spare for each girl, and since I only run the washer every few days (with only 2 people), I only get a clean bottle every few days. Not a good excuse, but its the excuse I've got.
Sunny was a horrible SOUP maker, and often landed poops from above in her water too. She would dump and dump and dump pellets in there. She still makes soup (we call it beak butter for some weird reason), she just loads her beak up with pellets, goes to the water bottle and makes the soup in her bottom beak. She also does this with cherios (though the hole!) and other foods that are dry. She sometimes clogs her bottle, pushing her food and tongue to the tube sometimes leaves pellets in there.
The only thing I can assume is that they like the sound it makes? Or they're using wild insticts to poo in the river which will wash down stream and not reveal where they live?