Cedarhurst-
Basically the halacha is that a woman’s words are not upheld in beis din (to demand a divorce) if she ‘admits’ to her husband that she cheated on him willingly, unless he believes her. The reason is that maybe she is just saying this because she wants to force him to let her get out of the marriage so she can be with someone else. If she wants a divorce that’s fine, but she has to go through the process like everyone else. The man, according to the din of the gemara, is believed in a parallel situation, without going into details. The reason he is believed, again without going into details, is because he has something to support his claim – that is, according to the din of the gemara, a man can force his wife to accept a divorce, so since he could’ve done that anyway, he’s believed with this claim. This is called “b’yado l’garsha ba’al korchah”. However, the Rema (quoting a Hagahos Maimonis b’shem the Ri M’gash) says that being that we have accepted Rabbenu Gershom’s cherem that a man may not force his wife to accept a divorce, he is no longer ‘b’yado’, and therefore nowadays he will need further proof of his claim to demand a divorce. My point was to say that if indeed a heter me’ah rabbanim is so common, then perhaps it should still be considered b’yado. After further thought however, I think that this may be a faulty proof, because there is a Tosafos Yeshanim in Kesubos 22a, which, while it is ambiguous, I understood it to imply that anything which requires the consent of others is not called b’yado. V’tzarich iyun.
Disclaimer: This has been written from memory.
As for the story, I’d rather not go into details. If someone understood, fine, and if not, I’m not really sure I should’ve posted it in the first place, so we’ll leave it at that.