70-200L zooming and center point moves?

Those of you with a 70-200L, when you are at 70mm and zoom to 200mm, does your subject in the center move slightly?

For example, if on a tripod and composed @ 70mm, in the center of my frame where the center AF point is I have an object. Lets call the object "x". If I zomm to 200mm (tripod stable, no sag, etc... it's a Markins M10 on a Gitzo), the "x" now is positioned at the top of the center circle in the viewfinder. This happens regardless of the lens pointing downward, level with horizon, or upwards.

Is my 70-200 the only one that does that, or is that an inherent characteristic of the lens? I never noticed it until now.

Which 70-200? There are three different versions...

70-200/2.8 IS

Could someone verify this for me please? Of all the 70-200/2.8 users out there, no one can quickly check out what I'm talking about?

So no one even cares about verifying this for me? I've searched, and cannot find anything on it. However, my search shows 100 people will respond to 200 threads on the diff between the 70-200/f4 and 70-200/f2.8.