Does the GroupBox Header in WPF swallow mouse-clicks?

Question

Have a look at this very simple example WPF program:

Answer 1

Ian Oakes answer stuffs up the tab order such that the header comes after the content. It's possible to modify the control template such that the border can't receive focus.

To do this, modify the template so that the 2nd and 3rd borders (both in Grid Row 1) have IsHitTestVisible=false

Complete template below