even if it were all a joke (and I think you're right, people often pretend something was a joke in order to wriggle out) there remains the issue that she's not listening to your advice, and not doing any practice. Perhaps if everyone is now in face-saving mode, a way out would be to suggest that since you both enjoy the choir and live in similar musical communities, and you feel perhaps your teaching style isn't in any case ideally suited to her (every pupil/teacher relationship is different - a good teacher for person A might be poor for person B, and vice versa) - overall it would preserve your friendship and give her better value for money for her lessons if she found a different teacher. No ill-feeling, just better that way. Hopefully you can go your separate ways without anyone feeling they've been left with egg on their face.
But DMC is quite right.