You're right -- by far, the product failures I see are caused by people who are self-focused (what do I want to make? what's fun?) vs service-focused (how can I serve people? create value?). Which is why I teach the exact opposite path:
http://unicornfree.com/2013/how-do-you-create-a-product-peop...
My students have cleared that one up already, I think :)
So let's address your #B — "what problems they have the authority to solve."
What is authority exactly? Who gives it? It's not really a term I use in the class because I think it's misunderstood. When Jaana wrote that she didn't have "enough authority," she meant reputation, not authority. But when you come down to it, it's not like Jaana is, say, a famous actress, who wants to break into rocket science. No, she's not famous or well-known at all.
Her real problem isn't authority -- or the perception of authority, or reputation, or trust. It's not a question of image but reach.
Her statistical chops are not at issue, only the size of her platform (readers, followers, fans). And she's working hard to fix that problem right now, using the "ebomb" strategy I teach in 30x500: Educate people, help them, and they will 1. read it, 2. share it, 3. remember you.
As you can see, since we're discussing her post and people are saying how useful it is, this strategy works :)
Now... if you have a platform already and you want to help people, serve people, and sell them something, and you're worried "They won't believe I have the experience!"...
Don't try to sell a teaching product. Don't let it rest on your judgment. Don't use yourself.
Instead, give them a tool that is "factual" -- "This is the math, just plug in your numbers" -- instead of based on opinion or your personal experience. This way you outsource the "judgment" to the end user of your tool. An alternate way is to do research and compile findings, and let the research speak its opinions instead of you.
In that way, Jaana did take my advice. :)