One thing that may be causing confusion and frustration is the way words like "database" and "account" and "user" are heavily overloaded when you look at all the different RDBMSs together.

I work with Informix mostly, and their use of "database" means something quite different from what it does in Oracle. In Oracle, you'd have an "instance", where you'd have a "database in Sybase or Informix. I don't know where Firebird fits into this, so it may be that the references to "database" were appropriate usage in the context of Firebird, but led you to erroneous conclusions based on your database experience.