Wand of Dowsing Secret

[Truly Contagious Laughter]

Scenario: While nearing the end of the game and rallying the troops, my friend played Wand of Dowsing. However, because he did not want us to know which card was chosen (the discard pile was quite large to do process of elimination), he secretly chose a card and would not announce which card he had chosen.

Question: Is this an acceptable play of the card? Or does the card being chosen by Wand of Dowsing need to be exclaimed for the knowledge of other munchkins?

Note: We ended up ruling he did not have to tell us since the card/rules do not specify, but I was not pleased with that ruling.