This is a fine example of the failure to apply logic in the law. If your assertion is correct, then the SC is engaged in an extremely clear-cut case of logical fallacy.
You can't prove a negative. You can only prove a positive, and the Constitution is constructed such that the burden of proof is on the would-be president to supply proof of natural born citizenship. If the SCOTUS has in fact determined that Berg et al must supply evidence of a negative (e.g. that there is no proof of a missing BC), then they are fools and illiterates in the ways of logic, and should all immediately be removed, disbarred, and tattooed across the forehead with the word "Fraud".
That’s the system. If you don’t like it, change it.
Um, I think that is the definition of “plaintiff,” i.e., someone who brings a charge based on evidence.