Like many other tyrannical governments, the Nazis twisted the religion of the country to their own means. The III Reich did not grow out of the church, it took over the church in 1933, after the rise to political power.
The problem with statements like yours is that they make it seem as if anyone who says they are a christian automatically gets whatever actions they take attributed to the religion. If you want to say that Christianity is responsible for the crimes in Nazi Germany, then what you are really saying is that the Nazi argument for the holocaust, world wars, etc is a valid argument within the precepts of Christianity. If you'd like to argue that, then go ahead, but otherwise the crimes can't be attributed to Christianity any more than I can attribute every crime committed by an atheist to atheism.