I would try a twilio test without the Laravel auth to see if that works.

I'm not sure if returning the xml header to twilio would make a difference or not, but when I did some twilio integration in the passed, I created the following helper function for the responses.

    /**
     * Prints XML response to twilio API caller
     *
     * @access public
     *
     * @name    response
     * @param   xml $cmd
     * @return  VOID
     *
     * @author Jorge Garifuna
     */
    function response($cmd)
    {
        /* Render TwiML */
        header("content-type: text/xml");
        echo "<?xml version=\"1.0\" encoding=\"UTF-8\"?><Response>\n";
        echo $cmd;
        echo "</Response>\n";     
    }