I have a question for you, Alan. If your partner is looking at a resting die with a "2" and the other one is a spinner, does he show you this or tell you this fact? Again, this situation would be exactly the same as if your partner telling you s/he only needed to look at one die to tell you "At least one of the dice is a 2". Yes, at that point the odds truly become 1/6.
It's not a good analogy for the original problem, though.