That wouldn't have anything to do with the pathing. CB Auto Actions doesn't pull the group id from the URL or anything of the sort when outputting GJ activity streams. The activity stream is actually there on the page. It is being hidden by CSS output from your template. Specifically the below.
IN: /media/plg_jchoptimize/cache/css/04c3107ac3c4542fa04d6e832dd36420.css
ON: Line 66
Code:
.tab-content>.tab-pane {
display: none;
}
Caching/compression error in your JCH Optimizer usage maybe? That CSS doesn't exist on the longer path.