William Shirer, in his Rise and Fall of the Third Reich, comes to your conclusion, more or less. The Einsatzgruppen(E), were far less trained than the armed forces. They also came in later, after the fight was over there, especially when any civilians might want to help, and get rewards for it.

The majority of them were bloodthirsty, a few were there for the pay, and a few just couldn't go quite that far, as in murder, themselves.

Being a member of the Nazi Party is not unlike being either a Republican or Democrat, except that there was no second party allowed. Unlike in the Soviet Union or present day China, where there is only the Communist party, and it is limited to no more than 10% of the population, the Nazi Party was open to all who qualified, and was needed for almost any job, if one was to work.