In other words, if the content profile node type settings are to display the full CP node on the user account page, this module works great. However, if the content profile node type is set to display only a link to the profile, then the condition is triggered only on the user account page, but not on the actual profile page.

I suppose that could be the intended use, allowing a second context with a path condition to actually handle the profile page. But that's pretty non-intuitive, and perhaps not helpful to a designer who is playing around with each option.