After a discussion, I was made aware of the following:

At Competitive and Professional REL tournaments, players are required to shuffle their opponents’ decks after
their owners have shuffled them. The Head Judge can require this at Regular REL tournaments as well.
I'm a bit confused about this though and would like some further information. Is a cut good enough? What happens if a player doesn't want to do anything to their opponent's deck? What are the penalties for this?