We're there such a thing as a "default history" I might agree that you have no burden to prove it didn't happen.
Arguably, there is a 'default' history - it's history. We just lack certainty about significant elements of it, and we alleviate that uncertainty in various ways, to various extents. We can't alleviate the uncertainty around the claims of the resurrection to any great extent, and so it remains an unsubstantiated claim.
But unfortunately there is no such thing as a "default history".
In terms of an 'default' status for the academic study of history, there is. Nothing happened is the default. Then there's a claim - say, "my hippy friend came back from the dead". Then there's a search for validation of that claim - "I have a really crap bedtime story that mentions it". That's a poor source, but we've worked with worse. Does the event in question require something more significant than that - it's a claim of magic, it requires a lot more than that to be accepted. Therefore, it's not accepted as part of the validated historical claims.
Lots of historical suggestions have left zero evidence.
If they've left no evidence there wouldn't be a claim at all. No-one is making claims about a King Kevin of Rickmansworth on the basis of no evidence, but they are (for instance) making claims of King Arthur based on old stories. Those old stories are retellings of earlier works, and on investigation it seems whilst there might be one or two early tribal leaders or warlords whose antics contributed to the collection, there is no 'King Arthur' to put into the record. Similarly, whilst it seems like there was arguably some sort of agitator/teacher on whom the Jesus myth is based, all of the magical bits are put down to mythologising after the fact.
Just because an event can be categorised as "naturalistic" does not guarantee it's having happened.
But classifying it as 'supernatural' gives good reason to think it sits somewhere between fairy-tale and outright bullshit.
O.