Yea thats not smart to try to put a sick animal in a box. You never know what they will do. Thats Poor advise. Now going out and staying a shovel handle away from it as u put it out of its misary would be alright. My great grand father always taught me those life rules. Dont let an animal suffer, never point guns at anyone (even in a joking manner), and One shot One kill!
I've had to use a shovel more then once. When I lived in the city it'* not like you can pull out a gun. If a squirrel or something was hit by a car I would pick up the shovel. One good bong and it was over.