I think the burden of proof would be dependent, not on location, but on who made the claim. For instance, if this Muslim declared to his colleague that "There is no God but Allah, and Mohammad is his prophet," he would have to back himself up. If he overheard a conversation between two atheists who were expressing their disbelief in God, and he wanted to contest that point, the onus would be on him to support his theistic worldview, despite the assertion that there is no God having been made by others, since he would be challenging the claim.

In the first instance, he made the claim, and accordingly, he needed to back it up. In the second instance, he also made a claim that a previous assertion was false. Had the original party asserted that the holocaust had never happened--there simply wasn't any evidence for it--and he had disputed it, the onus would still have been on him to show that they were wrong, since it was he who intruded on the conversation to add his input. The burden of proof could easily shift, however. For instance, if the Muslim man showed a photograph of the aftermath of a gas chamber, with a Nazi flag visible in the photo, and one of the holocaust-deniers said it was photoshopped, the latter would have to support his claim.

The reason I think the minority position has the burden of proof by default is because it is they who are asserting that most people are wrong in a particular area. If they want anyone to pay any attention, they have to make their case. If a member of the majority disputes one of the reasons given by the minority for holding their position, the onus shifts to the member of the majority to back up their reason for disagreeing on a particular point, and so forth.