in the root of your fuel installation (there where the oil script is). If you just load index.php, you miss the required functionality that is in .htaccess, which rewrites the request URL to something Fuel can use.
It gets there because it still goes to the 404 page.
How are you checking, using a browser? If so, the HTTP_ACCEPT from the browser header will override the json extension, if you want to skip that, you need to set "ignore_http_accept" to true in the rest.php config file in app/config.