Almost every smart consumer device these days runs Linux, so likelihood is your Viera is doing the same. While Linux can write to FAT32 and NTFS filesystems, for large files such as video recordings, either Linux XFS or JFS filesystems are far better. So chances are your TV formats the drive into one of these formats (or possibly into an ext3 or ext4, irrelevant really).

What you could do is download an install CD of Ubuntu Linux, these also have a CD live mode which lets you boot from the CD itself and run full-blown Linux, and it doesn't require any installation on your hard drive. Then plug the hard drive a spare USB port and see if you can read the disk content. When done, just shut down the PC, remove the CD and you are back in Windows in no time.

I finally got around to trying this, I have an LG HD Smart TV and have used the record function on it, I have a Live CD I use for repair and recovery, which has saved me a lot of heartache by saving lost files etc, it's this one...
http://www.runtime.org/data-recovery-live-cd.htm

When I boot to the Live CD it can see the Folders on the drive I recorded to, but I can't see the files in the folders!
Everything I try to do I get 'Permissions Denied'
I've copied the Folders to another drive, and when I'm back in Windows the Folders are empty, I've given up for now!

Why do I want to do this?
My HD TV gives me better signal reception and I can watch TV in really bad weather, when the HD STB has given up and can't record anything, if I can find a way to see the TV recorded shows I want to cap on the PC, I'd not only be able to cap them, but the image may be a lot better because of the stronger signal, especially important with the crappy WIN network signal strength where I am.

Maybe my TV recording system is set up so that I have no way to do it...

All filesystems beyond very basic ones (such as FAT32) have concept of permissions and file ownership. What is most likely happening is that files are written and owned by non-privileged user/account configured within your TV but once that drive is plugged into your computer, unless you are an administrator (in Linux called root user), you can't read files created by another account (in this case account used by your TV).

Your data recovery CD is based on Knoppix, a popular live CD distribution. Not too familiar with it but I suggest you try and gain administrator/root privileges once it's booted (something like sudo or su command if running from a console), then try reading hard drive contents. If there is a file manager installed, see if it has a administrator/root mode to open file locations.