1) If your visitors are looking for something specific on your site, the Sitesearch will locate it within your pages before it finds it on the web (especially if it's a page that doesn't appear in Google's index for some reason.)

2) Some folks see the search box and simply start searching. They either don't pay attention to the radio button option to choose "Web" or "Yoursite.com"; or they're not really sure what changing the selector does, so they just search with the default settings.

But the increase in CTR probably has to do with what users are searching for. Instead of searching for generic material over the web, they're likely searching for something very specific to your site.

Just my theory.