This setting only changes the time format in the calendar, not on the whole site. The description is a little misleading as it says "You can choose to see times in either 12 or 24 hour format for the whole site." which makes it sound like a global change, although admittedly it is in the calendar section of the settings.
The time format is tied to the default for the site language, if one wants to change this from the default is has to be done manually in moodle/lang/lanconfig.php, not a very user friendly method. Making it harder is that I couldn't find any instructions in the Moodle Docs for how to do this.
I notice that there is a patch to enable this in the GUI - see http://docs.moodle.org/dev/Timeformat, it looks like a perfect solution - but alas it hasn't been integrated to Moodle yet.