So in your opinion there is no explanation for the words of the later authorities who answered the Ketzot HaChoshen’s question? (There are, of course, many other simpler and more understandable answers to the Ketzot’s point.) He asked: how can it be that if a woman said, “I was a married woman and I am divorced,” and afterward witnesses come and testify that she was a married woman, then the migo is canceled and she is now considered a married woman? After all, at the time she made the claim, she had a migo, so how can the migo later disappear? She already had credibility. And to that the later authorities answered (Rabbi Nachum, if I remember correctly) that “the mouth that forbade” is different, because the whole rule of “the mouth that forbade” is that if you want to accept the forbidding part, then you must accept it together with the permitting part. Therefore, when I have another source for the forbidding part, I no longer need her. So there is no explanation for those words of the later authorities? (Sorry for the length.)

Correct. It really does not make sense to me. I could answer the Ketzot HaChoshen in several other ways.

Could one perhaps say that with migo, I believe your current claim because you had credibility with the claim you could have made? Meaning: if you had claimed “forged,” then I would have believed you that the document was forged by force of your claim that it was forged (according to most medieval authorities, “paid” by way of a migo of “forged” is by the law of migo and not by the law of “the mouth that forbade,” unlike Nachmanides’ view). And if you had not claimed “forged,” then the document would have been valid. So because you have credibility regarding the claim of “forged,” I also give you credibility regarding the claim of “paid.” But in the case of “I was a married woman and I am divorced,” the reason we would treat you as having the presumption of being unmarried is not because you claimed that you are unmarried, but because ordinarily every woman has the presumption of being unmarried until proven otherwise. In other words, the credibility is not in your claim but in the reality, namely that ordinarily every woman is unmarried, without tying it to your claim. Therefore, when you say, “I was a married woman and I am divorced,” I would not believe you in that claim, because even in the claim you could have made, you did not have credibility.

That is a formal explanation that assumes migo is the power of a claim (or the power of credibility). But simply speaking, the credibility to claim that she is unmarried—even if it is based on a presumption—is still credibility. Likewise, in the claim “forged,” I would be believed because I am in possession of the money, and still there is credibility here that gets transferred to the claim “paid.”

I agree that in both cases—both “the mouth that forbade” and migo—I am believed; it is just that this power of credibility is on a certain level (let’s say, the level of “why would I lie?”), and that works very well in monetary law, but in matters of prohibition involving sexual relationships it does not help. Therefore, if I accept the “I was a married woman,” I cannot accept the “I got divorced” merely by force of migo; I need something additional (the explanation of those later authorities), and that falls away when there are witnesses.
(And one should not object from the analogy between monetary law and matters of prohibition involving sexual relationships, because obviously the whole analogy applies only when I am opposing the presumptive holder, not when I am together with the presumptive holder; after all, one witness is believed when there is no presumptive holder, and likewise in other such cases. And every migo, at least according to a significant portion of the medieval authorities, is not in a way that extracts from someone else—in other words, the presumptive holder is always on the side of the migo.)