OK so I did something kinda different...I had this pool which surface was 1 z level ABOVE my hospital. By channeling in like 3 successive z layers, I brought the water from above the hospital to BELOW my hospital, filling a new pool 1 z layer below it.
So I put a well over this new pool (well @ hospital level, water 1 level below)...
"Urist McIdontCareAboutMyWoundedFriends cancels give water / clear patient: No water source."
Me: "aww, come on...oh, I got it! I'm gonna make the well a water source zone"
"Urist McIdontCareAboutMyWoundedFriends cancels give water / clear patient: No water source."
Me: ...
While writing this, a possible answer to this problem occurred to me:
There are stones at the bottom of that pool I made. I forgot to dump them...there's no stone on the tile directly below the well, though...so this should work, right?

P.S.: Two consecutive goblin ambushes. My two best fighters were sleeping. My military now consists of those two guys, and one fellow who made it to the hospital. The hospital that no patients have managed to walk out alive from...yet!