it's not what they believed, it's that "protecting germany" in the way national socialist propaganda explained it is inherently tribal. if they, as you say, joined out a sense of protecting their country, and if "protecting their country" as espoused by the national socialist was inherently tribal, wouldn't that make the soldiers tribal? sure, you could say that the soldiers were ignorant/didn't regard poles, russians, jews, or the myriad other groups the massacred human, but that doesn't mean they aren't tribal.
But remember, it wasn't only racial purity that made them power-hungry. It was the desire to control, to dominate. I still fail to see your logic. It's not to say that they joined to promote and realize racial purity. I see how, technically, the military was under the control of the government, which the national socialist party happened to have control of. However, that does not automatically make each individual tribal, because the point of the military is to better and defend the country, not necessarily to realize an agenda. Take it from the guy who was there.