I think this is then a more general limitation of the mocked liburl in tests.

Technically, not a full copy is needed, but I think the engineering costs around generating a fake file (and associated catching of the specific test use-case) are greater than that of chipping the full CSV file into Nilearn.
This statement is true conditionally to the fact that several examples behave that way, otherwise the engineering costs associated with handling the current `nilearn_data/data` directory management are then greater.

Should I open an issue about that?