I got Hardy Heon installed on a old computer with a second harddrive that is unallocated so I created a small vfat partition.
Then I double clicked the vfat partition, a pop-up came with policy changes and I was asked for password.
The vfat partition now mounts to /media/disk at every boot and I got full rw access, I am guessing it's a hal and gnome-mount thing.
It's now added to - Administration > Authorizations > hal/storage > Mount internal drives.
No entry was made to fstab.
So my suggestion is to comment out the vfat entry you made in fstab.
Then umount the vfat drive and see if the above works for you.
I was however able to mount /sdb1 to /mnt with full rw -
/dev/sdb1 /mnt/vfat vfat auto,utf8=true,umask=0000 0 0
The drive didn't show under Computer but is was there, I really think your suppose the mount in /media.
Finally fat32 is not that great for many reasons so going with something else might be the thing to do anyway.
Just to add,
you would probably only need a fstab entry if you wanted to bypass the defaults.
to not auto mount but be able to mount as user.
/dev/sdb1 /media/vfat vfat users,noauto,uid=1000,gid=1000,utf8=true,umask=000 0 0
opps! Come to think of it you are running xubuntu so you might be missing out on some gnome features.
If that's the case,
/dev/sda3 /mnt/disk vfat users,auto,utf8=true,umask=000 0 0