New Zealand Law
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Have you seen any medical certificate? It could be a problem that no response was made to this when she offered, but I believe she may be able get one as many doctors would happily give an employee a certificate saying she was too stressed to work. But you could put her to the test and ask for a certificate. If she refuses then you are justified. If she does get something, you would need need to balance what she can do, as against the possibility she may not pursue this. She would need to bring a personal grievance over the one days pay, which may not be justified having regard to the cost. But then there is cost for you as well. So I suggest ask for the certificate and then decide if you want the risk of a personal grievance.