how can you test the 'catch all route' using ordinary controller tests? - ruby-on-rails-3

Question

Note: As per RafaeldeF.Ferreira's suggestion, this question has been heavily edited since its original form.
My JSON-based app needs to return something sensible when given a bad route. We already know that the following rescue_from ActionController::RoutingError doesn't work in Rails 3.1 and 3.2:
# file: app/controllers/application_controller.rb
class ApplicationController < ActionController::Base
protect_from_forgery
rescue_from ActionController::RoutingError, :with => :not_found
...
end
(This is well documented in https://github.com/rails/rails/issues/671.) So I implemented what José Valim describes in this blog entry (item 3), and details are provided below.
But testing it has been problematic. This controller rspec test:
# file: spec/controllers/errors_controller.rb
require 'spec_helper'
require 'status_codes'
describe ErrorsController do
it "returns not_found status" do
get :not_found
response.should be(StatusCodes::NOT_FOUND)
end
end
fails with:
ActionController::RoutingError: No route matches {:format=>"json", :controller=>"sites", :action=>"update"}
Yet this integration test calls ErrorsController#not_found and succeeds:
# file: spec/requests/errors_spec.rb
require 'spec_helper'
require 'status_codes'
describe 'errors service' do
before(:each) do
#client = FactoryGirl.create(:client)
end
it "should catch routing error and return not_found" do
get "/v1/clients/login.json?id=#{#client.handle}&password=#{#client.password}"
response.status.should be(StatusCodes::OK)
post "/v1/sites/impossiblepaththatdoesnotexist"
response.status.should be(StatusCodes::NOT_FOUND)
end
end
So: Is there a way to test the 'catch all route' using ordinary controller tests?
implementation details
If you want to see the implementation, here are the relevant code snippets
# config/routes.rb
MyApp::Application.routes.draw do
... all other routes above here.
root :to => "pages#home"
match "/404", :to => "errors#not_found"
end
# config/application.rb
module MyApp
class Application < Rails::Application
config.exceptions_app = self.routes
...
end
end
# config/environments/test.rb
MyApp::Application.configure do
...
config.consider_all_requests_local = false
...
end
# app/controllers/errors_controller.rb
class ErrorsController < ApplicationController
def not_found
render :json => {:errors => ["Resource not found"]}, :status => :not_found
end
end