We don't need to access the root directory.
Perhaps that you have setup something that require to go in the root directory.
Perhaps a "tmp" directory that you have setup to go in the root like "/tmp" or any other things

If you ask that, I suppose that you know the path that cause the problem and to help me understand your remark, please provide the value of the path to understand what is tried to be accessed in the root path.

I had the same issue on a server with Plesk 12.

I changed the open_basedir to 'none' at was then able to install the patches.

Kind regards

-Stephan

We don't need to access the root path of your server but if you have setup an open_basedir, you have to provide the permission to access the slave site directories and also the master directories.

So you may potentially have to put several path in your open_basedir to give the access to the master and the slave site.
Otherwise, effectivelly the "infinite loop" can occurs inside Joomla when a directory can not be created.

The fact to put the "/" in the open_basedir is equivalent to disable it.