I recall a TV show saying that sometimes Kindle's break down and that there is nothing can fix them. Models (it said) seem to have only a limited operational life.
You can of course buy a refurbished model, but they are picked from certain models that had specific faults that were fixable, but sent back under warranty. A new model being sent out to the person that returned it. If your Kindle was out of warranty. The Amazon people would be under pressure to encourage you to get a new one, hence the reply. But that is my opinion. I think the company on the whole is very good at customer service. But I doubt it is set up to encourage repairs of out of warranty items.