This happens when the debaters' personal level of knowledge and expertise has been exceeded by external sources introduced to the debate. Essentially, then, each person is using an appeal to authority with different ideas of what level of authority their sources have, since it well beyond their abilities to verify their sources' arguments. Terms like Epistemic Closure in political contexts address the related phenomena of conflicting but self-consistent networks of authoritative sources.

I'd call the underlying issue an "Epistemic Divide"