Call privacy is intrusion blocking, Private Caller is blocking your CID...
The Private Caller feature works, no COS change necessary, internally and for external calls as long as your carrier supports the ISDN or SIP message to mark the number Private, just dial the Private Caller FAC, followed by the number. Just learned it this week, not sure how long this feature has been there, but I was always told previously you couldn't do this.
Works just like *67 on your cell phone, and that is the FAC we set for it at the location it was implemented this week.