Creating a Database for Joomla!
From Joomla! Documentation
I think this page needs to be updated to reflect the fact that, if you have a database user with create access, you do NOT need to create the database first. You only need to have or create a user with full access as shown in the screen shot. Once you've done that, instead of creating a database, you can simply put the name you want used for the new db into the field in the joomla installer and joomla will create it for you.
I had no idea this was even a feature until today, so I think we need to have it in the documentation.