For at least one DNS server I've setup (I don't know much about it, to be upfront) all requests for which that server did not have an authoritative response were simply forwarded to an upstream ISP server. Maybe this is an atypical setup, or I'm describing a different problem to the one you're envisaging.

"Make it your upstream provider's problem" isn't a very helpful piece of advice if you're running that provider, I suppose!