Very true. I have had one duckling, and one turkey end up stretched out face down in tiny poultry waterers. Not sure how...it's like they go to get a drink and lean too far In and then I assume breathe in a bunch of water. Because really enough water to breathe into your lungs can drown you it doesn't have to be deep, but something with sense will get out of the tiny puddle of water.
Have never had chicken do this. But I also keep all my waterers raised now...on a cinder block or flat slab of wood. That seems to stop them from getting their whole bodies in there and freaking out.