I think there is no way to assign a user group to an organization in Liferay 6.1 and thus the depiction in the User Guide is wrong and should be corrected.
I intentionally placed this thread in the "suggestions and feature requests" category in hope that someone from internal Liferay team could follow up on it as I didn't find a way to report this issue directly from the user guide (ability to add comments? ability to send feedback via email? any other way?)
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The structure of roles, users, groups, site, organizations etc and possible relationships between them is rather complex and unless one is building a complex portal with many users, only a small subset of these features is needed.
To clarify this area for myself, i created a simple membership diagram - see attached image. (arrow means "can be direct member of" and is transitive. Roles are not included)
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