Fraid not. Judge land pointed out to her that she, or more properly her client, is the one making the accusation, so the burden of proof rests with her.
That said, it doesn't mean that discovery won't be allowed for her to obtain that proof.
BTW, she only needs to prove that BHO is not a natural born citizen, not that he was born in Kenya and not necessarily that he was born in any other foreign country. Of course proving that he is not a citizen at all would probably be easier and more straightforward than proving lack of natural born status, since if one is not a citizen, one can hardly be a member of the subset of citizens who are natural born.
I understand that the plaintiff normally bears the burden of proof. But this is a case where the defendant (Obama) has blocked or seeks to block access to decisive evidence (his long form BC and/or other documents) that would establish or negate his constitutional qualification as NBC to be POTUS.