This is at least a plausible approach, but it's usually a cloak for holocaust-denial-lite, much as intelligent design is a cloak for creationism.
It may be that there wasn't a single master plan to exterminate the Jews in camps. However, there was a policy to round up all the Jews in Europe. When the war was over, vast numbers of them were dead. (I'm not sure of the proportions). It's possible to claim that they didn't kill them by gassing or execution - but regardless, they died because the Nazis wanted them dead.
The German Army rounded up many thousands of British and American servicemen as prisoners of war. In spite of the shortage of food, and Allied bombing, they managed to feed them throughout the war, and most of them survived. It wasn't the case that circumstances made it impossible to keep them alive. The Jews could have been kept alive. They were killed instead.