It's not interesting to know which groups people have joined
I know what you're saying here. In theory a User could join multiple groups without too much thought. ( a mouse click )
Admin assigned groups 'some' should have the option of being automatically displayed, and maybe only admin assigned roles. This integration would give better handling for what @psychobunny is mentioning, with mobile/ipad integration.
I guess you could say, user groups and admin groups (roles?) are very different, and perhaps should not be displayed as user 'groups' under the groups page. Separated perhaps ?