I did some more testing.
I had a new Domain account log into the W7 computer. That account was, by default, a "User" and not a member of the "Administrators" group.
I found that the new account could create NEW folders on the USB drive and could read existing files, but could not delete existing files. Basically, since the new account had no special rights to that USB drive, he/she could not do anything that would change existing data, but could freely ADD files and folders. This is typical behavior for most folders on a Windows desktop or server.
Using my (Administrator) account, I gave the new user MODIFY rights to one of the existing folders. I got a strange error message, but the change DID seem to take effect. My new user can now delete files that were already on the disk or were subsequently added by another user.
So if you want a new user to have rights to the ENTIRE disk, you should just have to go into the Security properties of the disk and add "Modify" or "Full Control" rights to the entire disk, making sure you propagate the changes to the lower level folders, too. Otherwise, go through the folder list and change the Security properties of the individual folders, allowing downward inheritance when appropriate.
I just did that with my USB drive, giving "Modify" permissions to the new user on the entire drive, and it worked fine. The new User can now delete everything on the drive.
The behavior I'm seeing doesn't seem different than what I'd expect from XP Professional, except for that one error I got (saying that my account, which is a member of "Administrators", doesn't have permission to add Security rights for a folder, but it seemed to work anyway.)