I went to the source and asked one of Canon USA's top two tech guru's, the great Rudy Winston, about the "AF Home setting." By the way another forum question asked how to get feedback to Canon. Simple, send Canon USA a letter or email. They are interested in what photographers have to say and they pass on the information and requests to HQ in Japan.
Wish I was going to the Olympics, but won't be this year! Have to file that under my "hope to do it in the future" list.
Anyhow, the solution to what you're experiencing isn't intuitive -- but it will work, depending upon how much you want to instantly move to other AF points. If you've gone into Custom Controls and configured the Multi-controller (joy-stick) to let you immediately move AF points about, by default, it acts as you describe: use the Multi-controller to move to some outer AF point, stop, and then press the Multi-controller straight in, and it returns you to the center point. But, if you press again, it reverts to the previously-selected AF point. Sounds like that's not what you want.
My 1D Mark IV, with "Multi-controller while metering" (C.Fn III-9-1) active, actually behaves the same way the 5D Mark III does, allowing you to use it to move anywhere off-center, and then toggling between the last memorized point and center as you press it straight-in each time.
Two basic options to get around this -- sort of -- on the 5D Mark III:
1). ONLY use the Center AF point: Set the Multi-Controller for direct AF point selection within Custom Functions; actually use the Multi-controller to navigate to the Center AF point, and tap the shutter button to lock it in. Now, each press of the Multi-controller (straight-in, not at one of its 8 angles) will simply stay at the center point. However, I doubt that's what you're asking about... otherwise, there'd be no need to use the Multi-controller in the first place.
2). MEMORIZE a frequently-used off-center AF point (you can only memorize one at a time, however) by navigating to it -- you can use the Multi-controller, or press the rear AF point select button, and then turn the top/rear dials to move to some off-center point you expect to use frequently. Press AND HOLD IN the rear AF point select button, and while you're holding it in, press the top panel illuminator button (small button wiht light bulb icon, on upper-right of top plate) -- you'll see "AF HP" appear briefly, indicating "Home Position" (you've memorized that AF point.
Now, NAVIGATE BACK TO THE CENTER POINT, using either the Multi-controller or combination of AF point select button and top/rear dials. The memorized point blinks on and off in the finder, letting you know it's there and can be accessed with a push of the right button (more on that in a moment). Pressing the Multi-controller straight in keeps you at the center AF point, no matter how many times you press it.
To instantly return to the memorized point: configure either the AF-On button, AE Lock button, depth-of-field preview button, or Lens AF Stop Button (select EF super-tele lenses only) to act as the instant return button for the memorized AF point. For AF-On or AE Lock buttons, select "Metering/AF" icon, then press the INFO button, and in the new screen that appears, select the "HP" option and press SET. With the Depth-of-field preview button or Lens AF stop buttons, select the HP option (no need to press INFO first), and press SET. Now, when the chosen button is pressed, you jump to the memorized, off-center AF point... either let it go, or (with the latter two), you can set it so that another press on that same button reverts you back to where you started from (Center AF point).
In the meantime, the multi-controller can be used to jump you back to the center point if you've set the DOF or Lens AF Stop buttons to jump you to the memorized point and require another press to return you there. But if you simply press the Multi-controller straight in, you're back to having it toggle you between the last two visited points (center and memorized ones). You can defeat that by pressing the AF point select button, using the Multi-controller to move one point off-center and back again, and then pressing it straight-in.
But aside from this, I don't see any way, on either camera, to use the Multi-controller to freely move off-center, and then press it straight-in to get back to center in one step, without having subsequent presses toggle you back and forth to the outer point you'd previously moved to.
Not sure if this helps, but I hope it does!
-- Rudy Winston