BuddyPress.org

You can’t remove it as an action, since bp_get_displayed_user_nav() is a template tag and not an actionable item.
If you’re using a child theme, remove the calls to bp_get_displayed_user_nav() or try hiding the menu via CSS.

*Edit – Just thought of a sneaky way of doing this.

Add the following to your theme’s functions.php:
http://buddypress.pastebin.com/90L4iKve