The documentation in this case is wrong. All variables in /etc/default/grub start with GRUB_, so it's GRUB_DEFAULT=saved, not DEFAULT=saved. I've corrected the Ubuntu wiki to reflect that.
The official grub manual describes this correctly: http://www.gnu.org/software/grub/manual/grub.html#Simple-configuration
Put the following in /etc/default/grub:
GRUB_DEFAULT=saved GRUB_SAVEDEFAULT=true
Then run:
sudo update-grub
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