The AP is Just plainwrong
So is Mashable. According to Mashable, the AP Stylebook is changing "Web site" to "website". Mashable swoons over the decision, insisting that it's long overdue, because, after all, if the language isn't twisted out of shape, it's not cool. Right? (OMG! Its da c00lz!)
What part of "a server on the World Wide Web" says common noun? In that context, Web is a proper noun--period. Sure, you can run an http server that isn't accessible to the Internet (yes, capital-I Internet). So what? It isn't part of the World Wide Web, then, is it? It's an intranet server. (Or maybe the AP would prefer intranetsite. Come to think of it, I wonder if this aptweet was posted from their twitteraccount and echoed to their facebookpage before it ended up in the mashablepost?)
Here's the World Wide Web Consortium's mission statement, complete with capital letters. And here's Time Magazine's Time 100 article on Sir Tim Berners-Lee.