Hmmmmmm, it appears you are talking WebRing even though you refer to groups. When you join a *ring* and place the navigation code (which really is code to request the navigation code not really the navigation code itself) the system displays the navigation code it has on file for that URL which is derived from the ring(s) the URL is submitted to. If you subsequently change the ring(s) associated with that URL (by leaving one, joining another, etc) the system will *eventually* display the correct (set of) navigation code for whatever ring(s) you end up in. It isn't instantaneous, however, which is the frustrating part for those of us who expect things to happen right away. It can take a few minutes, sometimes more if it's busy. In some cases the system seems to botch it altogether and you have to "nudge" it into action via the URLs page in your My Account area by "rebuilding" or "re-ordering" the "stack" as it's called.
Perhaps if, instead of displaying navigation code geared to the ring(s) one joins, it displayed navigation code geared to the website, but with the appropriate links for the ring being navigated, the rendering could be done in a more real-time manner since it would be done when the site is registered rather than each time a site is added to or removed from a ring.
Just a thought.