Switch backend controller tests to request tests

[scottohara]

(from http://rspec.info/blog/2016/07/rspec-3-5-has-been-released/)

For new Rails apps: we don't recommend adding the rails-controller-testing gem to your application. The official recommendation of the Rails team and the RSpec core team is to write request specs instead. Request specs allow you to focus on a single controller action, but unlike controller tests involve the router, the middleware stack, and both rack requests and responses. This adds realism to the test that you are writing, and helps avoid many of the issues that are common in controller specs. In Rails 5, request specs are significantly faster than either request or controller specs were in rails 4, thanks to the work by Eileen Uchitelle1 of the Rails Committer Team.

[scottohara]

Could be done as part of #139?