Yes, ultimately they do (usually) and yes, you are missing the point.
"filesystem as a database" is not referring to database software that stores the data on disk but rather that the application is directly interacting with the filesystem. Imagine dumping a JSON document to disk, then reading it from disk, compared to storing a JSON string in a DB. Sure, they are both backed by the disk, but one is not "filesystem as a DB".
"filesystem as a database" is not referring to database software that stores the data on disk but rather that the application is directly interacting with the filesystem. Imagine dumping a JSON document to disk, then reading it from disk, compared to storing a JSON string in a DB. Sure, they are both backed by the disk, but one is not "filesystem as a DB".