Avoiding all police/authority interaction is wise, not immoral.
Morally, you owe those people nothing.
Every interaction with them is an opportunity to destroy your life or the lives of your family.
I agree. That said, it depends on this guy's house/ranch. If the odds of a random discovery are low, shovel and shut up.
I've had a black bear come into the kitchen window, almost making it into the house before my wife ran it off. If one ever does make it inside and I kill it, I will have the same dilemma. If I can just remove the carcass and go about my business I will. If enough attention was attracted it's going to cost me a lot of money for simply defending my home and that disgusts me.
In GA its like the end of the world if you kill a bear. Its like killing the last passenger pigeon. Never mind that we are lousy with bears here. If we ever have to kill one its going in a large hole out in the back forty somewhere.
Shoot..
Shovel...
Shut-Up.
A wise old saying here.