Yes. Normally, problems give you information so that you can do something with it. Otherwise, even if the author says later on:

Notice that the problem condition gives the suitor a certification about the truth of the labels

the problem author can always cop out and say "yes, but the certification itself was meaningless!".

If I take the labels to their face value, the treasure cannot be in the green box because the red label doesn't have a truth value. (If it's true, then there are two true labels, therefore it must be false. But if it's false, there is only one true label, so the red one is true.)