Integration tests just mean you are testing the integration of multiple components, say view and controller, model and database, controller and model. Acceptance tests are tests from the end-user's perspective and touch the entire stack like a real user would. Acceptance tests are integration tests. It's alright for these tests to hit the database because part of what you are testing is the integration with the database.
I say "higher-level" tests to refer to integration, system, and acceptance tests, because I don't have an opinion of where to draw the line for FactoryGirl. Is there a reason you would consider FactoryGirl for acceptance tests, but not integration or system tests? Just curious, because I might learn something.