Thanks for the link; it's certainly informative, but it discusses local storage, not databases...the subject of my original post.
For an explanation of databases see
FURTHER READING > Web SQL Database: > Introducing Web SQL Databases, and, for an example, "Web Database demonstration" (which reproduces the pop-up that CNET generated).
In the end, though, and although I realize that both databases and local storage expand Safari's functionality, I'm still not sure how they differ or what benefit I'd derive from, for instance, allowing CNET to create the database it asked to create.