[See post I & II] The starting point for the halacha of a wife who confesses being prohibited to her husband for adultery (or rape in the case of a cohen's wife) - is the Mishna (Nedarim 90b). This Mishna records that historically the normative halacha was that women were believed when they made such claims and thus the husband was required to divorce them and give them their kesuboa. However at some point in history, the halacha was changed because it was assumed that they might be lying in order to obtain an automatic divorce as well as the kesuba - because they wanted to marry someone else. The Rosh explains that the generations deteriorated and women now had no qualms about lying in order to get divorced and marry someone else. These sources clearly indicate the nature of marriage and divorce as well as the change of halacha in the face of social and psychogical changes in society. There is obviously much more - but this is the foundation that everything else is built upon.
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Nedarim (90b/Yevamos 112a): Mishna: Originally it was ruled that there are three situations in which the wife must be divorced and also receive her kesuba. 1) When she said, "I am defiled to you" [i.e., she is prohibited to have sexual relations with her cohen husband because she had been raped - Rashi] 2) "Heaven is between you and me" [i.e., she claims he is impotent which is something private that is known only to them and G‑d - Ran]. 3) "May I be removed from Jews" [i.e., she took an oath not to have sexual relations with any Jew because it is difficult for her- Ran]. However later the because of concern that whoever made such assertions was not telling the truth and was interested in another man and could be assumed to be causing damage to her husband – the Rabbis changed these rules to the following. 1) If she asserted, “I am defiled to you” – then she must bring proof before her husband would give her kesuba and divorce her. 2) If she asserted, “Heaven is between you and me” – then it was suggested that persuasion be used to reach a mutual decision. [He should be persuaded not forced (Rashi), or prayer to have children (Rabbeinu Tam) or a banquet to placate her to stay or that he should give a get (Yerushalmi).] 3) If she said, “May I be removed from Jews” – the husband was now told to nullify the oath in regards to him [view of Rabbi Yossi while Chachom hold that it should entirely be nullified] and she could stay married and take care of him while remaining removed from Jews.
Tosfos Yom Tov (Nedarim 11:12): Her claim is not accepted because of the concern that she is interested in another man. – perhaps she will go to another place where she is not known and despite her oath that prohibits all men – she will marry another (Ran). [ Therefore the law was changed so if she said] “I am impure for you”, we don’t believe her unless she brings proof for her claim. We should note that if she claims that she was raped she is in fact prohibited to her cohen husband - as the original psak indicated. The obvious question regarding the changed psak is, what happened to the fact that she is prohibited to him that we require her to stay married to her husband - unless she can bring proof? A possible answer is that whoever gets married does it conditionally according to the understanding of the rabbis. Therefore when she announces she was raped and thus prohibited to him, the rabbis annul the marriage retroactively and thus she was in fact an unmarried woman at the time she was raped. However this answer only makes sense if she claims that she was raped by someone who doesn’t invalidate her for a cohen. But if she was raped by to someone who invalidates her to a cohen, she would still be prohibited to her husband even if she was unmarried at the time of the rape. Since this mishna makes no distinctions as to who raped her – this suggestion that the marriage was annuled can’t be the answer. An alternative answer as to why there is no prohibition for the cohen husband to be with a wife who claims to have been raped is that the First Teaching was not based on the actual halachic but on a chumra (strigency). That is because according to the strict letter of the law the wife is definitely not believed to cause the marriage to be ended when she says that she was raped. That is because she is subordinate to him. Rather the reason that she was believed when she said she was raped is because it is very embarrasing for her to state such a thing. And the First Teaching says she is to be believed because if it weren’t true she would not degrade herself by saying it. Therefore it is the Second Teaching which says she is not to be believed is according to the strict letter of the law. These two answers are from the Ran (Nedarim 90b). Tosfos writes that since there is concern that the wife might be lying when she says these claims because she wants to marry another man – the Sages have the power to uproot all prohibitions. I also wrote this explanation in their names in the beginning of the 10th chapter of Yevamos. And this is also the language of Rashi in the 4th chapter of Menachos that I cited in the Edyuos 4:10.