A quick update...
I thought I would try to increase the size of the Independent Disk while it was attached to a production VM. I did this in the same way you would increase a disk on any VM (a PUT request with a new copy of the VirtualHardwareSection) but it threw an error of "The attached disks on VM 'MyVM' cannot be modified.". I thought it might be the case, but this confirms that Independent Disks must be detached from a VM before they can be increased, which is a bit of a shame.
Still, the original question still stands.... why isn't vCloud Director increasing the disk size when I do so on a detached disk, despite the task appearing to complete successfully?
I'm in danger of answering my own question here, but for the benefit of anyone who ends up via through Googling...
I've just re-read the documentation at Create or Update an Independent Disk and it says:
"To create an independent disk, you must specify its name and size. You can optionally include a description and specify a storage profile to be used by the disk. After you have created the disk, you can modify its name, description, and storage profile. "
It doesn't actually say here that you can increase the disk size - so perhaps you can't. I think I might raise it with VMware Support to see if they can confirm either way.
Also looking at the VMware vCloud Director Cookbook may help. There is some good examples.
Hope this could help
So, the reason I was not able to resize the Independent Disk was that I am on vCloud Director 5.6 and the ability to resize independent disks was not introduced until vCloud Director 8.