It's controlled via the unity-greeter draw-user-backgrounds key I think - but the one belonging to user lightdm, not the user whose background it is displaying
If you want to play with it and see, you can do something like
com.canonical.unity-greeter draw-user-backgrounds true
to view the current value, and
sudo su -s /bin/sh lightdm -c "gsettings get com.canonical.unity-greeter draw-user-backgrounds"
I don't know what greeter is used for cinnamon - gtk-greeter? - or whether there is an equivalent parameter
sudo su -s /bin/sh lightdm -c "dbus-launch --exit-with-session gsettings set com.canonical.unity-greeter draw-user-backgrounds true"