Crazybob,
Incorrect. They are two totally different parameters and have different actions.
allow_url_fopen
This option enables the URL-aware fopen wrappers that enable accessing URL object like files. Default wrappers are provided for the access of remote files using the ftp or http protocol, some extensions like zlib may register additional wrappers.
open_basedir
Limit the files that can be opened by PHP to the specified directory-tree, including the file itself. This directive is NOT affected by whether Safe Mode is turned On or Off.
When a script tries to open a file with, for example, fopen() or gzopen(), the location of the file is checked. When the file is outside the specified directory-tree, PHP will refuse to open it. All symbolic links are resolved, so it's not possible to avoid this restriction with a symlink.