Admittedly, it's a bit unclear as to what is happening, but maybe this will shed some light.
Illustrator does have a setting called "snap to point" -- but it doesn't tell you WHAT snaps to the point, does it? Prior to CS4, Illustrator always snapped your CURSOR to the point -- not the point you dragged. So if you grab an anchor near its edge, you snap the edge of the anchor to another point. I know, this is totally silly, right? It only SEEMS like zooming in help because when you're zoomed in real close, it's much easier to grab an anchor from its center.
In CS4, Smart Guides can now snap OBJECTS to other points. Meaning you can grab a rectangle from its right side and have the left side snap to a guide or another point. This matches the behavior of InDesign by the way.

Mordy