Prevent viewing of content profile node, but allow on user page

I'm looking for a way to prevent users from viewing a content profile by going to node/[nid] directly, but still allow them access to viewing it on their user page. I'm using the content access module for this content type. My problem seems to be that when I prevent access to viewing the the content profile node type, the user can no longer view the profile from the node/ or user/ path.

The documentation for this issue seems to be a bit misleading:

The module uses drupal's content or "nodes" for user profiles, so the access
 permissions applied to view the content profiles are the regular node related
 permissions.
 That means the "access user profiles" permission of the user module still
 applies only to the user account pages at "user/UID" but not to content profiles,
 which can be viewed at node/NID too. Still you can use any regular node access
 module to restrict access to your content profiles, e.g. you may use the Content
 Access module for that (http://drupal.org/project/content_access).

I was hoping this meant I could prevent users from viewing individual nodes, but viewing the content profile embeded on the user profile page would be okay. Is this not possible?