Yes, the back button is broken because it forces the user to think how things work.

In your example, if you left IE, instead of starting it again from the home screen you should hold the back button to enter task switcher and jump into running IE instance from there. After that the back button will work ok.

Which is counter-intuitive - tapping tile on the start screen should either give you the same experience like jumping in the app from task switcher, or start new application instance.