Two teams work on two different components of a project. Team A works on component A, and to keep things simple, Team B works on component B. The system needs both components to function.
There's an additional catch. Team A needs component B to test A. Team B needs component A to test B.
So what to do? Well they would do what any good team would. Team A goes on holiday while Team B finishes and then Team B relaxes. Unfortunately that isn't always possible.
Instead, they would use mocks, whether they create their own stubs/fakes or use an existing framework. To verify that component A works, Team A uses mocks to replace component B's functionality. Team B uses mocks to replace component A's functionality. All tests pass.
The next step would be to integrate the two subsystem and put it in production. I mean surely if all subsystem tests pass, it should work......the reality is it probably won't.
The moral of the story: Two halves don't necessarily make a whole. Don't skip your integration tests. It's not a waste of time. And integration tests aren't just about running all your unit tests on a continuous integration server. They are integration tests, not isolated unit tests.