Inserting a 2GB thumb drive on my 8.04 (your Feisty Fawn is 7.04), I
get the identical display with Properties, but one thing you omitted
is what's at the top of the Properties box: "Owner". On mine it displays
"Owner: thad - Thad Floryan".

What does yours display?

This is a stretch, but what kind of filesystem is on your USB devices?
The thumb drive I just tested is "FAT" (not "FAT32" or "NTFS" or any
Linux filesystem).

I'm able to copy files to the USB thumb drive using either the command
line or copy'n'paste.

A "df" shows the USB thumb drive as "/dev/sdb1" automounted on
"/media/THUMB_2GB" (I relabelled all my thumb drives after removing
the "U3 Smart" junk).

A quick workaround may be to simply burn a CD or DVD with your data.