there is a time to do what is right and just keep quite about it.
Yup, situational ethics. I have had several talks with different game wardens about the issue of killing big game animals to put them out of their misery. Shoot, shut up, and drive off is not a very bright idea. That type of behavior wastes a lot of resources when the animal is found and reported. Worse yet, if you are seen shooting a big game critter and drive off, the ensuing poop storm can be a PITA.
For all the game warden knows (based on the report) is you may have just committed a drive by thrill shooting. Happens a lot in Wyoming. By all appearances you may be thought to be guilty of taking an animal out of season and wanton waste. All of that can be avoided by one phone call.
I won't condemn anyone for dispatching a crippled critter. I have done it more than once. But I always got permission first, or reported it after. Avoids a ton of hassles.