According to your title, you are trying to say that, Every person can solve every other person's problem. But not his own problem. That may not be true and that is not what author is trying to say.
He is talking about the (smart) people who can solve other's problem. But not about all the people.
Thanks for the clarification. Looking at the discussion here itself is a validation for the article at some level. It is a simple article presenting conclusions from a series of interviews with reasonably smart people.
The conclusions are being over-analyzed which is the characteristic of very smart people. HN is a community of such smart people and I am not at all surprised that it is being over-analyzed here :)
He is talking about the (smart) people who can solve other's problem. But not about all the people.