I think I understand why the unit tests in Rails were confusing me. I had assuming that unit test fixtures ran YAML into some kind of in-memory activerecord object. But in reality, fixtures will put data into a test database and then unit tests will interact with it.

As far as I understand it:

1) An integration test is one where the test code goes outside the realm of the class and has a dependency on an external entity.
2) Databases are external entities.
3) Fixtures will write to the test database.

Therefore:

Any test containing a fixture is an integration test, even if it's in test/unit and extends Test::Unit::TestCase.

Furthermore:

Unit tests are tests that can be run in isolation, in any order, without any external dependencies.

Whew. Had to get that out of my system.

Not that I don't understand the rationale; or that using fixtures could be extremely handy. But a spade is a spade.

As usual, as soon as I realized the underlying issue, there was no shortage of help, Jay Fields being the most helpful.