I don't measure to the 32nd of an inch but when I am measuring tight I will mark it fat between the 16th's to compensate for the thing-a-majig on the end of the tape. I also glue that thing so it won't move because it will move enough to mess you up.
That movement of the stop/hook is there for a reason. The amount of slack should just about equal the thickness of the stop/hook. It allows you to get a reasonably close measurement whether you are measuring an inside (pushing against) or an outside (hooked on and pulling) measurement.