I may be all wet (sorry, I couldn't help myself!), but I have never heard that it is unsafe to shoot a high power centerfire bullet with a body of water in the line of fire. What about firing a high power centerfire bullet with a rock in the line of fire? Don't rocks likewise deflect bullets? Perhaps the key question is what is the backstop rather than whether water is present. If an elk is standing in a 100 foot diameter lake, I'm not suppose to shoot at it, but it is OK -- safety wise -- if it is standing on the shore beside the lake? I'm not sure I understand.
As far as ethics, why is it unethical to shoot big game standing in water? The preferred method is to shoot the animal, while it is standing still, while it is not excited, and while it is totally unaware of the hunter's presence, and it is best if one bullet dispatches the animal promptly. If the animal is running after you shoot, you may want to consider whether the chances are you scored a hit on the first shot. If you think it was a clean miss, the ethical course would be to pass on the running shot. I think if you cleanly missed the first shot on a standing, unsuspecting animal, odds are you aren't going to connect with a running shot on the animal. If you DID score a hit, of course, you need to try to bring that animal down, thus you ought to shoot again.
One important consideration involved in the question of shooting big game animals standing in water is the question of how will you recover this animal if it drops dead on the spot? This is an important consideration for moose which are huge, have long legs, and do often stand in water. It seems like it could also be an important consideration for elk. An elk, I suppose, could stand in 3 feet of water, be shot, drop on the spot, and yet be impossible to difficult to drag out of the water. What then?