It might not have been an issue with database permissions but file/folder permissions. If setup cannot setup the config file because of that, it fails to add the database credentials. You can edit it manually via FTP. You find the file in zp-data/zenphoto.cfg.php on your install.
But if you get such permissions issues, you might run into further ones as the albums are filesystem based, too. In case you do you might need further help from your host. Here is information about those permissions: http://www.zenphoto.org/news/permissions-for-zenphoto-files-and-folders/