I’m not opposed to having organizations as "members" of social networking sites, but I can understand why some people wouldn’t want them. I think it would be cool if the organizations had to add a flag to their page that said they were an organization and if users could have the option to auto-block all members with this flag set.
This way the organization’s message/buddy request would only go to people who wanted to read it and people who didn’t want to be bothered wouldn’t have to worry about having to deny/read requests or messages they already knew they didn’t want.
I think there are lots of good ideas on how to seperate them, but I think seperating the two profiles so they can be distinctly identified is preferable to eliminating the "groups". I’m sure there are people who enjoy these groups, or they wouldn’t have so many buddies.