In my case I didn’t have control over php.ini as it was locked down by the hosting company. They had a link in the open_basedir setting and nothing matched. It’s a bit dangerous (will need refitting after every update) but I solved the problem by changing inc/class-file.php to add:
$open_base_dir = realpath($open_base_dir); // gwss 20151125
just before
$part = substr( $file, 0, strlen( $open_base_dir ) );
It’d be nice if something like this could make it into a later release.