Hi,
Just to say I never quite resolved this as a custom setting - so just hid all enrolments by default on the profile page. Students can still see their own courses under 'my courses' but not what other students have taken.
As a bonus I have to say it reduced number of requests from students to be removed from open courses they'd browsed into once and never used again (I set course list to display frequently used content at the top).
Regards, Gordon.