Hi @jonocas!
I took a look through the different API calls that can be used with quizzes (surveys) and wasn't able to return the information you were looking for. However there is another option. You can click the option for quiz statistics when viewing the survey and click the option for student analysis. That will give you a file that should contain their responses for the survey question matched to their name.
This guide goes over what is available from that interface.
