Stories only appear to people who are able to view that specific content, based on privacy setting...
Stories only appear to people who are able to view that specific content, based on privacy setting chosen by the person who posted it. For example, if you comment on a friend's status, then only people who are permitted to see your friend's status will see a story about it when they view your Wall.
You cannot prevent all stories from being published on your Wall; however, you can:
Prevent people from seeing certain stories by editing individual privacy settings for content you post. For instance, you can prevent a friend from seeing a story about a photo album you publish by preventing them from being able to see your photos.
Remove individual stories by clicking the "X" that appears to the right of the story after you move your mouse over it.