Same as my answer to how routing affects isOpen(), $site::activePage() (which is a method, not an object) uses $site::page(), which returns $site::page. Use site()->visit($uri) in your router to set $site::page to the original uri.
EDIT: Sorry - just read the docs page for Omitting the Blogs Folder in URLs that you linked to and the example in the code already does this. Have you modified that code in any way?