If the file system is vfat then you can not use "chown" or "chmod" to change file permissions. FAT/32 simply doesn't have any mechanism for permissions. So, the permissions and owners are emulated when the file system is mounted and they are applied across the entire file system. On my system (Fedora) the default ownership on an automounted file system is set to the user who is currently logged on at the console. If nobody is logged on the ownership is set to root when automounted.
If you didn't want to change any configuration files you could unmount the file system and mount it manually with whatever options you wanted:
# umount /dev/sdg1
# mount /dev/sdg1 /mnt
or when you do the mount command set the ownership and permissions:
# mount /dev/sdg1 /mnt -o uid=500,gid=500,dmask=0000,fmask=0111
This would set the owner and group to your ID (assuming your ID is 500, see /etc/passwd or use the "id" command) and it would set the directory permissions to 777 (rwx) and file permissions to 666 (rw).
On my system the default permissions can be changed by modifying the /etc/udev/rules.d/50-udev.rules file. The hal daemon actually does the mounting and as you already know the desktop environment you use also has an effect on automounting:
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EDIT: Now I am confused. I just stuck my thumb drive in and mounted it vfat and for some reason "chmod" actually works and appears to change the permissions on the files/directories just as it would on an ext2/ext3 partition. I don't get it. This has never worked before and it "shouldn't" work. I have no idea what is going on there.