No reason to lie about it, Tony.
Theres a difference between the two scenarios, in my opinion.
To me theres a difference between retrieving downed game and staking claim to a tree on someone's property. If I shot the animal legally on MY property (or property I had permission to hunt) I should be able to get that animal.

I'm not going to let it rot simply because the neighboring landowner wants to be an ass.
But again, thats just me.