Well, that's down to the Joomball cookies extension.
Components Anywhere renders the component using the 'component.php' subtemplate (&tmpl=component in the URL).
You could ask the Joomball developers if there is a way to not let it render on those urls/pages.
1. Do you know a good Cookie extension that doesn't have this conflict with your CA?
2. Is there a way to use your Advanced Module Manager miracle to whitelist those requests as Joomball is a module. (hide module on these hidden menu requests or something like that.)
Well, the debug module position is probably the only one also included in the component subtemplate.
It is not meant for modules other than the debug module.
See if you can assign the module to a position other than the debug. Optionally add an extra module position to the index.php of your template.