Well, historically speaking, there's certainly more to it. The Suwa war was largely the gods of heaven taking supremacy over the gods of earth. If Heaven had the power to say, "You're bound by this now!", there never would have been a Suwa War. And somehow, I doubt the likes of Suika or Yukari can really be considered a part of that system to begin with, so it wouldn't only apply to people already under their suzerainty.