^ ... Okay, you need to think in more general terms...
The water that we drink on Earth has been everywhere... I mean everywhere. Down the sky, in drains, from contaminated areas, the ocean, behind people's bums and other unpleasant areas etc. And guess what? We still drink it. It's to survive and the cycle starts all over again.
This is the same with Hyrule. The water doesn't have to come all the way from Zora's Domain. It rains in Hyrule and it contributes to a large percentage of the water source.
I'm saying that it doesn't really matter that the water source comes from the King's behind. He is a fish person so he would be a lot cleaner that the average Hylian that would sit there. And hey, Link walks through areas where there are dead people and blood from enemies and his boots are splashing all over the place in Zora's Domain. Now that's contamination...
I wonder if he orders his followers to wipe his bum, or does it flow away, it still wouldnt clean him very well though would it? but why care, if water cleans your bum then its better than paying for a butler ey?
Hyrule Castle is connected, or at least I could have sworn it was... The river just goes through some grates, but it's all the same river...
In the crazy lands between awakening and sleep, I wait, and I think on everything Zelda.
"Let fear be cast into the hearts of our enemy.
Let them lose all hope and let their heart sink into the unending darkness.
Let them have no will to live.
Let them feel the power of the Sages of Despair!"