Daf Yomi Nedarim 15a: Rabbinic Bal Yachel

Citing my Rif translation:

15a

אמר רבינא לעולם כדקתני ומאי בל יחל דרבנן
ומי איכא בל יחל דרבנן
אין
והתניא דברים המותרים ואחרים נוהגים בהם איסור אי אתה רשאי לנהוג בהם היתר כדי לבטלן שנאמר לא יחל דברו

Ravina said: In truth, it is as we taught, and what is "he shall not break {his word}?" Rabbinically.
And is there a Rabbinic "he shall not break?" Yes. As it was taught: If there were permitted things and others practiced in them prohibition, you are not permitted to treat them as permitted in order to nullify them {our gemara: rather than "in order to nullify them," "in their presence"}. For it is stated {Bemidbar 33}: "He shall not break his word."

These two variant readings perhaps carry different implications. If as our own gemara, `i `ata rashei lehatiran bifneihem, the implication is perhaps to conduct oneself according to the heter (for perhaps they might not understand this is a matter of difference in minhag), and thus you are nullifying his (=the other persons word = דברו). Perhaps like by certain fats where this is so, such as mentioned in Pesachim 51a, about the fat upon the yeter:

When Rabba bar bar Chana came {from Eretz Yisrael to Bavel} he ate of the stomach fat which is upon the yeter {= דאייתרא}:
To explain: there are two regions in the fat which is above the keiva {stomach} - one on the keshet {=lit. bow, the curved side of the stomach}, and one on the yeter {=bowstring, the straight side of the stomach}. That which upon the keshet is forbidden and that which is on the yeter, there are some who treat it as forbidden and some who treat it as permitted. And in Bavel, they treated it as forbidden, and when Rabba bar bar Chana came from Eretz Yisrael to Bavel, he would eat the fat which is upon the yeter in accordance with the custom of his place {=Eretz Yisrael}.
Rav Avya {רב אויא - our gemara has רב עויא סבא} and Rabba bar Chanin {our gemara: Rabba son of Rav Huna} entered to {visit} him. When he saw them, he covered it. They came and related {the incident} to the father of Shmuel. He {=father of Shmuel} said to them: He {=Rabba bar bar Chana} has reckoned you to be like Cutheans.

According to the girsa in the Rif, perhaps this is a deliberate attempt to nullify a minhag. Really it is permitted, but people adopted a stringency. But if people in general stop practicing it as stringency, this is the new custom, and it would nullify their words in the future. But this is bal yachel, on a Rabbinic level, of his (=some third person's) words, that is adoption of non-mandated stringency.