I think we are mixing the two concepts (unit and integration tests) but that's okay by me. If we weren't mixing them, then in theory, we shouldn't be doing anything browser related (clicking buttons). That should all be saved for midway tests. But the fact of the matter is that it's quicker to do these tests inside the unit tests.

I think writing tests is one of those things that, if you make it too strict and put too many rules around it, people will just stop doing it. It's better to have a loose definition and more tests then a strict definition with fewer tests. This may impact performance down the line, but right now my concern is just getting tests in place.