It is true that they could resurrect the tapes if they had a compelling reason to do so. Denying the request indicates that they don't believe the reason to be sufficiently compelling to warrant the extra expenditure of resources. That is subtley different from "we don't want to", which implies a level of capriciousness.

Government departments get FOI requests all the time and they take resources to fulfill. FOI is not intended as a way to have taxpayers fund people's pet projects. That's why FOI law doesn't require your government to spend (even more) money to acquire technology they don't have or need for anything other than the FOI request itself. Rather, something that requires that kind of extra effort and expenditure should be submitted as a research request, normally with its own funding.