She’s the one making the allegation, so she has the burden of proof.
So you don't know squat about the American legal system, do you.
This is under Civil Law, which is a preponderance of evidence. In other words, she is the plaintiff and Cain is the respondent. Which therefore places the burden of proof on Cain. That is, if this were actually a filed case. Which it is not. In addition to that, if this woman was out for extortion, she would not have made it public. So, money is not her motive. The consensus is, that she was notified that this anonymous affair between her and Cain had been discovered by the press, so she came forward voluntarily to protect her own interests.
In essence, she has already presented the details of the case first, with tentative evidence to support her claim. (Text messages) All they have from Cain is an informal denial. That is hardly an admission of innocence to any court, so the burden of proof is on Cain, which he cannot yet refute.
This is just getting started. And with just one month away until the primaries, Cain has no chance.