(Mishnah): Initially, they said that there are three cases of women who leave (Beis Din forces their husbands to divorce them) and receive a Kesuvah:

She says 'I am Temei'ah (I was Mezanah, so I am forbidden) to you';

'Shamayim is (a judge) between me and you (that you cannot father children)';

'I am withheld from [having Bi'ah with] all Yisraelim.'

They retracted, lest a woman put here eyes on (desire to marry) another man, and ruin [her marriage to] her husband;

One who says 'I was defiled', she must bring a proof to her words. (If not, she is not believed);

'Shamayim is between me and you', they do in the way of request (he tries to appease her);

'I am withheld from all Yisraelim', he annuls his part (what pertains to him), and she has Bi'ah with him, and she is forbidden to all [other] Yisraelim.

(Gemara) Question: If she did not bring a proof to her words, obviously she is permitted to her husband! (What is the Chidush of the Mishnah?)

Answer #1 (R. Heila): Is it not reasonable that if he is a Chaver (pious), he will be concerned [for her words, even without a proof]?!

Answer #2: If he is a Kohen, she is forbidden to eat Terumah (and even so, she is permitted to her husband. We explained this like OHR ZARU'A Hilchos Yibum 615.)

A case occurred in front of R. Chananyah, the colleague of Rabanan, and he permitted her to eat Terumah. (Her husband must feed her, so she cannot forbid herself Terumah, which would obligate him to feed her Chulin, which is more expensive.)

(R. Chagai): My father knows that the episode from the beginning to the end. Soldiers entered the city, and a woman came and said 'a soldier hugged me and cast semen between my legs (had Bi'ah with me - PNEI MOSHE)', and [R. Chananyah] permitted her to eat Terumah. (CHASAM SOFER (90b) - there was a place to hide. If not, all women in the city are forbidden to Kehunah!)

A case came in front of R. Yitzchak bar Tavlai, of a woman who said 'my shepherd enticed me (he told me that Zenus with him will not forbid me).'

He said 'is the shepherd (a Nochri) not Pasul?!' He forbade her.

Question: Here you say that he forbade her, and here (the case of R. Chananyah) you say that he permitted her!

Answer: Here she came to forbid herself [to her husband], and he permitted her (she is not believed at all). Here she came to permit herself, and he forbade her. (We explained this like TZIYON YERUSHALAYIM.)