Ketubot 24 - Collusion
A similar case to two women testifying about each other is where two Kohanim are testifying about each other that they are indeed Kohanim. If one says, "I am a Kohen," and the other says "I am a Kohen" - we do not believe him. But if they testify about each other, they are believed.
However, Rabbi Yehudah disagrees: we should never establish a person as a Kohen (to allow him to eat Kohen's portion) through the words of one witness, and especially here, where they may have colluded to testify for each other.
But is it true that Rabbi Yehudah suspects collusion? Didn't we learn this case: if two vendors of produce come to a town, and one of them says, "My produce is not properly tithed, however, his produce is" - we do not believe this testimony, because we suspect that in the next town they will say the reverse, and this is a ploy to inspire credibility; and here Rabbi Yehudah permits to buy their produce. But he should suspect them and forbid it!
Explained Rav Adda bar Ahavah, "Someone has learned this ruling about vendors wrong. He exchanged the opinion. Exchange them back, and Rabbi Yehudah is the one who suspects collusion."
Abaye said, "No need to exchange opinions! Rather, here it is different, because vendors are selling doubtful tithes, "d'mai", and this is not such a strict prohibition, so Rabbi Yehudah believes them anyway. Then how do the Sages disbelieve? - They say that if he has his wares, weights and scales, it is obvious that he denigrates his produce only because of collusion.
Art: Fruit and Vegetable Stall by Frans Snyders