I disagree. This has nothing to do with intelligence. It is all about connecting different domains of knowledge. You know and have experienced things they haven't.
Now you listen to their description of the problem, and transfer it to your domain of knowledge:
"Hey, this sounds exactly like an issue my friend Josh had a few weeks ago."
This is also why stories of the "king asking the farmer" or "CEO asking the cleaning lady" are so common --- it is all about the point of view.
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Where I agree with you is "listen first, speak later". Don't interrupt until they have finished telling their story.