Two instances where it's proved useful for me:
1) I create a lot of data on my office machine (or, worse, my boss does — I'm a sysadmin), then log out for the weekend. Anything I did in the hour before I logged out will not be backed up. If something goes wrong over the weekend (and doesn't it always?), that data gets lost.
2) The first backup I made of my staff's computers took a very long time as a full backup had to be created. We therefore let the initial staff backups run overnight, when our staff is normally logged out. This hint allows us to let them log out as normal, rather than having them use Fast User Switching to switch to the Login Window, which is easier and more straightforward for both them and me.

There are other times this could be handy:
1) You create some data on your machine remotely, via SSH or SCP, and want that data to get backed up, but you're not logged into the GUI.
2) Your machine acts as a server of some sort (file server, perhaps) and is rarely logged in to the GUI, but you still want to use Time Machine for backups.

Oh, and just to clarify, this should work for all external drives — firewire, USB, eSATA, what have you.

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