Assign people to organizations, or organizations to people?

We're designing a system that allows administrators to create an infinite number of users, and create an infinite number of organizations.

Most users will only belong to one organization, but some belong to more than one (and it might be necessary to remove a user's access from all organizations quickly). An organization might have just one user, or many. There's also a little hierarchy involved, where a user could belong to a parent organization, or one/all of its children.

There's a little debate: Is it better UX to assign organizations at the user level, or users at the organization level? Either way, we're thinking it's best to provide access to the information in both places. But if you could only choose one place for setup and editing, which would you choose, and why?