Fascism provides a specific permission structure for genocide that isn't present in other systems. That's not to say genocide didn't happen before the term was coined, but that the characteristics of fascism; nationalism, racial supremacy, military supremacy, victim complex, out groups, scapegoating, disdain for human rights, etc.; tend to be present anywhere that genocide is present, and genocide doesn't just happen because some "genocidal regime" found its way into power.

Whether or not you need their permission to make the policy; you need the people's permission for it to stand, because ultimately you need the people's voluntary compliance in order to carry it out. Otherwise you undermine your own system and generally incite resistance against it.