Storing the information isn't the real challenge, structuring the connections between different pieces of knowledge is what seems to be the very difficult part.
Without the latter, you can have all the data in the world, but no way to make any use or sense of it.
Let's start with your statement: "If it can store and retrieve data, it's a database." One of the notable characteristics of human memory is that it is not reliable. It does NOT reliably retrieve the data that it stored -- and I don't just mean that we forget some things, I mean that many of our memories are factually incorrect.
Human memory is extraordinarily USEFUL, but in order for the term "database" to have a useful meaning, I have to categorize human memory as a form of information storage that is NOT a "database".
Data is messy. The only thing you can do with it is preserve the original format that was used to record it, transform a copy to a format that's useful for the analysis you want to do, and join it to other, similarly messy data.
Wikipedia is a perfect example. It's messy as hell. It's blobs of data with connections between them. Most of the blobs are unstructured text (or at best semi-structured) but there are a bunch of images in various formats there, and links to outside datasources in myriad formats and locations. There are some standards and attempts to maintain order, but the whole thing is damn difficult to process by machine. It's a very, very long way from the Semantic Web.