They did these things, but there is a huge difference in intensity. Basically, the German troops in Western Europe by and large were still under orders to ight a war much like people understood theconcept. That included a gooddeal of what we consider atrocities today, and especially the SS was well known for its tendency to marry incompetence with savagery, which the leadership did nothing to discourage. But even later, when they committed horrors like Oradour and the mass forced recruitment of slave labour, they did so punctually, in defined incidents, as it were. I know it's not saying much, but a French prisoner of the SS suspected of being in the resistance was treated no different from a German suspected of being part of the KPD. In the Soviet Union and Poland, the atrocities were policy. Not only were Wehrmacht troops told not to prevent them, they were encouraged to commit them. There is an eyxewitness account by a junior officer who cleared out a Ukranian farmstead to quarter troops. An old man came to complain, and he had him shot. His daughter, the farmer's wife, started screaming, so an NCO clubbed her to death with his rifle. Now three young children were all alone in the world, and the officer, deciding to solve the issue, had them shot, too. This kind of thing would have had consequences in France or the Netherlands except in the last days of the occupation. In Russia, it was SOP. The incident wasn't even reported.
I think the problem is the long mythology of 'clean Wehrmacht', coupled with NATO's reluctance to touch on painful issues too much. The German invasion and occupation in Western Europe was not 'clean'. it was pretty atrocious, all told. People who hear of those things for the first time are shocked and assume that nazis were all the same everywhere. But they were, by theirstandards, behaving 'reasonably'. The war in the USSR was as close to hell as human ingenuity could devise.