Really? His title-winning Dortmund teams were miserly as fuck, thanks to, as you said, his signing of two world class centrebacks in Hummels and Subotic. Obviously they get looser in the later years - but I wouldn't say that Dortmund were the same from Day 1.
I would also argue that we way we play now is already very different to the way we played in season 1 under Klopp - he's seems willing enough to change the game plan if necessary. He's obviously not the worlds greatest defensive coach - but it can't help when trying to polish turds such as Lovren, Moreno and Clyne.