You say it's the wrong interpretation because you don't want it to be. In simple English it is the correct interpretation.
Two dice have been rolled and one is a 2. The chance of the other die being a 2 is 1/6 just as if that second die were a spinner on a craps table.
You guys cannot present the 1/11 answer with two real physical dice unless you combine results for two dice throws. You can't do it with one dice throw.
That's where your 1/11 answer does not apply to the original question the same way it doesn't apply to a spinning die on a craps table.
You were caught. Admit it. Or keep whining.