Is knowledge both sufficient and necessary for understanding, or is there another case?

When we look into our common use of language or linguistics, a sentence like “I know why x, but I don’t understand why x.” Or, I understand x, but I don’t know x.” Intuitively, it may seem strange. What does the person even mean when she’s saying that? 

But imagine a hypothetical case where a fireman reports to the father and his child on why their house burned down. The fireman states it was caused by faulty wiring. So now, both the child and the father know why the house burned down. But there still is an epistemological difference between them. The father understands why, whilst the child does not.

Is better understanding just due to having more knowledge about how or why faulty wiring in this case started a fire? So it is not so that understanding is anything different from knowledge? 

But it seems like while you can’t get understanding from testimony, you can get knowledge. Understanding depends on more internal processing to be able to reason or apply, which testimony alone will not suffice for. There are cases that suggest that a person can have understanding without having knowledge or justified true belief.

Imagine a person wants to learn more about the history of an Indian tribe, but there is only one book on the matter that is true. All other books or internet sources are nonsense and misinformation. By sheer luck, the person gets the book where the information is true. But also, the author was not knowledgeable about the tribe either, so that his guesses, fantasies, or obtained material happened to be correct was just by luck or coincidence. This person believes everything she read in the book, and everything she read happened to be true. If she can have “cognitive control” of the information, or reason with it, or apply it and understand how it will connect to another piece of true information, is there a genuine case of understanding without knowledge? 

Is knowledge both sufficient and necessary for understanding, or is there another case?