Activities marked as "Private" Don't leak. But in "enhanced privacy" mode your activities can be seen via the segment leaderboards. In any declared privacy zone, you stay off those boards, irrespective of options, and (allegedly) heatmaps. So really, it's "slightly more advanced privacy"
You can also opt-out of segment leaderboards. With some work you can lock out your account so only your friends can see your routes, photos and stuff. Everything is well explained on Strava support webpage in section called "Privacy Settings".
