You should always be on guard against a person who is enthusiastic to assign burdens of proof in any exchange, and the best way to be on guard is to remember this: Whoever makes a claim, has a burden.
If a man claims that God exists, the burden is on him to argue and provide evidence for his claim. And if a man claims that God does not exist, the burden is on him to argue and provide evidence for his claim.
And so on, with every claim around, until you start hitting axioms.
While you're at it, never accept the following excuses: "But it's impossible to prove a negative!" "It's really hard to show that something DOESN'T exist!" If it's extremely difficult to satisfactorily support a given claim, the proper response isn't to weaken the burden, but to weaken the strength with which the claim is committed to.