Of course you need to prove that NASA is lying.
Actually, I don't.
In a discussion on the existence of ghosts should the burden of proof be on the group mumbling "just because you can't see something doesn't mean that it doesn't exist," or should the burden of proof be on everyone else to prove that ghosts *don't* exist?
A company called Mollar International claims to have invented a flying car with safety comparable to a land vehicle, an outstanding performance of a 400 mile range, and sophisticated never before seen computer control. They claim that the Sky Car is ready to be mass produced if only they got a few more big investments. They've released a few videos of it hovering a short distance off the ground in test flights. Should the burden of proof be on the Moller proponents who are absolutely certain that all of Moller's claims are true, or should the burden of proof be on the skeptics who question the legitimacy of Moller's claims?
As we can see, the burden is proof is never on the skeptic. It's always on the claimant. If you claim something, the burden is on you to prove it.