Home page is getting current-menu-item even if it’s not home

Have you tried using the checkboxes / add Pages / add Categories rather than custom links when adding items to the menu? It’s sorta the opposite problem, but I’ve run into issues where WP does not recognize custom links as “this page” – maybe the fix is the same.

** EDIT **

I just ran across this thread in the WP forums which might help with your issue. Read comments from this point on down for a few suggested workarounds. http://wordpress.org/support/topic/custom-post-type-parent#post-1775314