It is mostly correct. Unless you sign very carefully worded IP assignment agreement to that effect, even work you get paid for remains under your own copyright. And frankly anyone who would sign that kind of thing on a employment test exercise is... Naive.

I doubt they paid for the interview work.

To be a work for hire, the work must be produced by an employee within the scope of their employment. Consequently, you cannot do work for hire if you have not been hired.