I assume you are talking about the SLM Status indicator on the Incident form. A user must have some level of incident user permissions to view the Incident form however no SLM or Admin permissions are required to see this information. I ran a quick test by creating incident where have at least one service target would attach to it. Viewing the incident, I could see the due date/time goal for the service target in the Status indicator and could click the link to view the service target details. I then logged as a different user that only had Incident Viewer permissions (no SLM permissions at all) and as this user I could see the same information. So if you can access the incident form then that user should be able to see the service target status and detailed information.
Hope this helps,