it gets even more interesting when there's a complete disconnect between what the website commissioner does/is and what their target audience are interested in and attracted by, and, when the website commissioner realises that and takes appropriate steps. a good concrete example: tampax and their beinggirl.com website (example taken from Groundswell book). basically the only connection between the decision to make the website tampax did, was the people/audience (15 y-o girls). beinggirl.com is a chat website about and for girls. it is not a tampax website, although it is in the sense tampax made it (and they let users know they're behind it without too much fanfare thus achieving what they wanted to achieve; recognition, good feeling -- it's taken on the same role as advertising). for most small businesses making a website not about themselves is preposterous. of course most small businesses don't have to take quite such extreme steps as the tampax example shows. rather than shift the subject/central focus completely away from themselves, just expanding the subject/central focus outwards is what's required. the site and its subject still encloses/covers them, but the site first and foremost is not about them but something bigger (but which they fall into). e.g. you're a builders merchants. instead of making it about yourself make it about building, how to use what you sell, common building problems and solutions etc.
in some book i read recently, new rules of pr and marketing by scott i think, there was this phrase: "think more like a publisher". i like that. imagine that flipped. imagine publishers making books with the same mentality as the typical small (and big in a lot of cases) business. e.g. the publisher faber and faber. their first book, its title would have been... faber and faber. and it would have been all about... faber and faber. of course just producing content which is attractive to some/any people (which is what publishers must do and do so) isn't quite enough in the case of websites and businesses. you have to aim and hit a particular type of person, because the type of person attracted to your content, you then want them not just to "buy" (visit, use, engage with) your content but then go on to use your company, and only a certain type of person is likely to use your company, so the content must be targeted. that's the part where most small businesses fall down. they make it about themselves for themselves. the "buying" of your content is an intermediate step, not the end goal.
the right hand side of the venn diagram linked to is still reasonably insular though. it's still all about the entity who's producing the website. in a lot of cases, including universities, this is probably logical and good, but in a lot of cases something wider, less insular, is appropriate. the key is to realising who's making the site and who the site is for are two very different bunches of people, and the people making the site will only benefit from the site if it serves the purpose of who the site is for. because if it doesn't they won't use/engage with it, and if they don't use/engage how on earth can it serve the purpose of those who are paying for it?