I assume your error is when trying to run the step2 of the upgrade. The logic is pretty explicit here
Code:
Content visible to verified customers only.
Example if the directory is writable
if ( is_writable( $newdir ) ) {
mkppdir( $newdir );
}
In your error this is triggered meaning the directory exists but is not writable
else {
if ( is_dir( $newdir ) ) {
$waserror = true;
print "The directory $newdir is not writable.<br />";
}
Your sysadmin could easily follow this logic and see what I mean.
Do they have any internal php commands locked down? I can take a quick peek if you have ssh.