Am I therefore to assume you are saying the burden of proof lies with the one making the claim?
I don't say it, but I recognize it to be correct in a legal and philosophic sense (onus probandi). Also, you can assume whatever you like, that's entirely up to you.
If that is the case and you were to say "God does not exist" could you prove that?
We're I to make that claim, then yes, it would be.