This is what checking "Search the internet" does (see the item just above the search box). If you uncheck the option, it does not show that item. It only controls that link in the Start Menu. The Start Menu is not built to actually search the internet. But if you use another method like opening some website/URL or shortcut to a website which may be added in the Start Menu by some program, your internet browser will open and you may be able to search the internet.

It doesn't mean the Start Menu searched the internet.