The Activity Stream in JIRA is at the moment showing information regarding all commit messages.

Users without access to projects mentioned on the Commit Messages still see the messages and are provided links to pages were they don't have access to.

This is a Privacy concern on instances with Restricted Projects.
On instances with a lot of dev activity, this generates unnecessary noise on the Dashboard.

Activity Stream should be restricted to the user visibility according to permissions. Commits from issues without access should be discarded.