Or some asymptomatic carrier administering a set of the test, or some of the cleaning staff coughing in the room before the tests.

That they focused on the person action (quarantines, tests) and not the environment (transfer shuttles, testing rooms, bathrooms and dressing rooms) kids hints the latter as a source. After all, you drop your mask during testing, and I've seen places doing it in a small, unventilated room with no pause between each person.