I like the thinking here. One strategy I have found to be somewhat effective in some cases is to take their question and begin to unwrap it. What questions can I ask them that help deconstruct their question, but more importantly, deconstruct their perceived challenge? There are any number of directions return questions can take the conversation, and the original questioner begins to see the value of the SE. They start to get that we, SEs, care about our customer's challenges and successes. Finding out the Why is a good way to dig a little deeper AND potentially uncover a new opportunity!!

At some point the conversation does get to a place where the appropriate response is "I don't know".