According to the documentation http://docs.sitefinity.com/inline-editing, any user with backend access and permission to modify and publish the pages should be able to use inline editing. The problem is it only works if you are an administrator.
Steps to reproduce:
1. Create a backend user and assign it every role except administrator
2. Log out of Sitefinity
3. Log in with the new user account.
4. Navigate to a front end page
5. There should be an inline edit icon.