Also, I referred to the field directly above the "Apache Directives" text area which is labeled "PHP open_basedir" and contains a bunch of directories which all point to the web root. Why doesn't this field actually do anything? phpinfo() still shows open_basedir as "none". Nothing is working for enabling open_basedir.
I'am sure that the field did what it should. Open the vhost file for this website and check if the line that you inserted into the apache directives field is in there.
So as long as you write sentences like "Why doesn't this field actually do anything?" or blame ispconfig for everything (by the way, why dont we blame intel or amd as they made the processor of the server so they are responsible for every operation done on this piece of hardware) for everything instead of asking for help, you can not expect that everone wants to help you with your problems. If you ask for help politely, you get a polite and fast answer. If you ask for help in a rude way, you get a rude answer or no answer at all.
This is in stark contrast to other forums like Joomla, phpBB and others, where help can be found readily from countless contributing members who aren't necessarily developers.
These cms systems are used by a lot of hobbyists that have the time to hang around in forums all day. ISPConfig is mostly used by ISP's that dont have the time to be in the forum or by poeple that istall it once and do not change things often when it works, so they are not here in the forum as well.
To come back to the original problem:
1) Post the top part of the php.ini output that shows if really suphp is used and not e.g. mod_php.
2) Post the part from the php.ini that shows which php.ini files are used.
3) Post the content of the vhost file of this website, it can be found in /etc/apache2/sites-enabled or a similar directory depending on the linux distribution.