I cannot for the life of me find the way to add a site wide recent activity stream menu item. I do not see a setting under the activity plugin options nor do I find one under the comprofiler section of the add new menu item options.

I am sure it is something silly I am doing wrong but I am deeply confused so any help you can provide would be great.

I know its 3 months since this post, but i had a similar problem just 2 days ago and found a way to work around it. I used joomla's Content-Load Module plugin. Here's what I did:
1. Created a new module using CB Content Module to publish the Activity Tab as module.
2. IMP: When publishing the module in the select position field i wrote in a custom position "activitytab" (shouldnt be any position of from any of your installed templates default or activated or in active)
3. created & published a new article in Joomla and with relevant titles (Recent Activity) user access levels (Registered) etc. and wrote in the plugin paramters " {loadposition activitytab} "
4. In the joomla Menu i created a new menu link as required pointing towards the article i just created (menu type single article)
AND it was there just like a normal component page.
P.S. While creating the menu i prefered to turn off all the article parameters eg. show author , show date, show link etc.