I understand what you are saying, and it's pretty close to what I wanted to say, but the sleepiness got the best of me. We just went about the same thing in 2 dif ways.

What I meant was this:
If the camera does not move, and the subject does not move, only lenses are traded, the depth of field will remain the same. Sure, a wide angle will cover more area than a tele, therefore having less magnification, therefore making for an apparent greater DOF.

But say the subject is a person, and 3 meters behind the subject is a brick wall.

Say you frame and photograph with a 50mm, say, at f5.6; and the brick wall is out of focus.

If you put on a 100mm, and do not move to recompose, you will get a tighter shot, sure, but the bricks on the wall will be just as much out of focus. (provided you stick w/ the same aperture)

Now, if you go back and put a 24mm, and once again do not move, you will cover a greater area, but if you enlarge the print enough, you will see that the bricks are still just as much out of focus.

Things to keep in mind:
bokeh might play a part in this, so comparing lenses of similar designs might be a more fair comparisson (I dunno)
the smaller magnification of the bricks in the 24mm shot might make them look more focused, so enlarge them to match the size of the 50mm shot.
The opposite goes for the 100mm shot.

Once you start thinking in terms of proportions, as glbeas said, it'll all be clear. It's all math... (not that I know it)

So, this long post is just to say: yeah, I know....