Say if somebody were to steal System of a Down's "Steal this Album", would they have any ground to stand on in that the item explicitly told them to do it? Would this fall under some form of entrapment?
The physical item is not the property of music group or the label---they merely receive proceeds in accordance with the contract. Rather it is the property of the retailer, who had to purchase it in order to put it on the shelf. Removing the item from the premises during normal hours is shoplifting, a type of larceny.
Criminal law is not suspended because an item's promotional materials might be (unreasonably) interpreted as an invitation to commit a crime.
Entrapment is an affirmative defense when law enforcement induces a person to commit a crime the person would have otherwise been unlikely to commit. Without law enforcement involvement, there's no entrapment.
An important point to note is that you cannot contract or otherwise deal outside the law. If an action is criminal then a private agreement cannot make it not criminal.
A person is in lawful ownership of an object cannot authorise someone to steal it - by authorising someone to take it they have transferred ownership by gift so the object was not in fact stolen. A person who does not have lawful ownership does not have the ability to give it away.