I don't mean defer all unit-testing until an integration test passes. The unit tests I'm referring to are those that verify that the SUT interacts with the 3rd-party mystery API correctly.
The rationale for deferring these unit tests is that they verify something that is unknown. If I don't know how the 3rd-party mystery API works, how can I even write a unit test to ensure that the SUT uses the 3rd-party API correctly? Only once some minimal integration tests pass do I actually know what behavior to verify.
Of course, all other unit tests should be written before the SUT is written in the usual way (red, green, refactor).