Just when I though I had finished reviving my parent’s computer with Ubuntu, I discovered that the normal user was unable to write to the shared FAT32 partition.
Much googling later, I found the solution.
fstab entry for offending partition:
/dev/hdb1 /media/MOUNT_POINT vfat user,rw,umask=000,uid=<username>,gid=<username> 0 0
From this thread.