That's it, thank you! It sounds like the smoking gun to me. We know from a patent filing that Google has mentioned the idea of tracking domain impressions (not just individual URL impressions). Just extend that to domain "clicks", but add in some ranking effects as a result.
Would be great if others can look for the same thing - I think the fat belly search terms may be an important part of this picture, rather than head terms or long-tail. And now the further question comes up - why would some domains be given this treatment?