The problem with that statement is that if you take away all the supernatural claims and give some room for creative embelishments and naming inaccuracies you end up with not just one but several "actual persons" but their existence becomes entirely irrelevant to the existence of a historical "Jesus".
It's a lot like the "god of the gaps": if you are willing to compromise on a definition of god that gives up on all supernatural claims in history and that only works through mechanisms indistinguishable from natural events, you're no longer talking about the same YHVH that painted fiery letters on a throne room, appeared in burning shrubbery, flooded the entire surface of the Earth and turned people into salt.
I think trying to argue about external facts when studying religion is largely a moot point. It's neat when you can tie religious doctrine and historical accounts together but a religion doesn't cease functioning because its historical claims are inaccurate. The historical claims are entirely accidental to the religion itself and should be viewed as mythological, not empirical.
I have met Christians who both understand that argument - that religion and empirical science belong to two distinct, separate magesteria - and reject it. But when I try to dive in to understand why, I do not ever understand their answer.
It's a lot like the "god of the gaps": if you are willing to compromise on a definition of god that gives up on all supernatural claims in history and that only works through mechanisms indistinguishable from natural events, you're no longer talking about the same YHVH that painted fiery letters on a throne room, appeared in burning shrubbery, flooded the entire surface of the Earth and turned people into salt.
I think trying to argue about external facts when studying religion is largely a moot point. It's neat when you can tie religious doctrine and historical accounts together but a religion doesn't cease functioning because its historical claims are inaccurate. The historical claims are entirely accidental to the religion itself and should be viewed as mythological, not empirical.