You did the right thing, too bad the original shooters did not finish their job. I had to do the same thing a few times down in New Mexico, and in Tennessee. I've also seen poor shots made, and animals lost from 40, 50, and 60 yards shots. The shooter did not know what he was doing, or did not care.
I shoot animals about the size of whitetails regularly at 300, 400, and 500, yards. I don't use a WHIZ-BANG-MAGNUM either, just a plain old 30-06, a 165gr bullet, and a good scope (currently a Burris). But I'm 100% sure of the shot or I don't make it. The only reason I don't shoot farther is lack of bullet performance.
I only use the magnum (.338/378 Weatherby) for Moose and Bears.