How does Google Instant change the referer sent by the browser?
Most of the time, a Google search result actually sends you to a Google redirect page rather than directly to the target page. They use JavaScript to switch the target of the link onmousedown as you click on it.
You can see this effect by click-and-holding on the search result link and watching your status bar.
This isn't specific to Google Instant, they've been doing it for quite a long time on their standard results pages.
The page anchor part of the URL can be manipulated client-side without a new request to the server. Even when talking about static anchor links (e.g. <a href="#foo">Section Foo</a>), clicking on them does not cause a new request to be sent to the server; it is processed completely within the browser.
The javascript being used by Google to make Google Instant work is simply altering the anchor programatically before making a request to the server.
What Google are you using?
My URL after searching is this:
It does include the q= part