The English rules tell you the order in which the dice must be resolved. It is not 'in any order.'
I just got my copy, and Paul is correct, the English rules actually give you an order...
Fellowship > Orc > Ring > Gandalf > Nazgul > Tree
... although I guess it's kind of moot because the only reason you'd want to choose your own order is to have Gandalf fire before the Nazgul do.. which, they do, so as far as the player is concerned the order doesn't matter. Maybe they just explicitly gave an order in the English version to clarify that you can't mark rings before you've checked to see if orcs cancel them.