This sounds really patronizing. I would be careful with that phrasing. People who don’t want their problem solved often know the solutions and don’t like the tradeoffs or change they entail. It is often not a knowledge problem.
It also implicitly discounts one of the most valuable processes: verbal processing. Some people, myself included, find themselves verbalizing a problem and the tensions in every choice and monitoring the logic and emotional response present in saying it out loud.
In this way, listening and solving aren't too dissimilar. Simply listening can give the speaker an appropriate environment in which to solve their problem. A listener can play a part in helping to solve the problem, but helping foster the environment in which the problem can be solved. Don't mistake this as a silver bullet, but simply recognize that being a listener is an underappreciated role and listener vs solver isn't as dichotomous as it sounds.
> It also implicitly discounts one of the most valuable processes: verbal processing.
Not really. The question, more generally, is: what should my role be in this conversation? Should I be an active participant in solving the problem? Or should I support you as you work through it?
I think the implication is that by listening passively you can be an active participant. That is to say, speaking the problem out loud causes it to run through alternate pathways in the brain which helps the person sharing their issue resolve their own problem.
As with so many things in life, the hard part is working out if your actions should be motivated by actually helping or feeling like you helped.
