The gemara in Rosh Hashanah 22b quotes a beraisa which tells the story of the בייתוסים trying to trick the chachamim into establishing the new month on the wrong date:
בראשונה היו מקבלין עדות החדש מכל אדם וכו': תנו רבנן מה קלקול קלקלו הבייתוסין פעם אחת בקשו בייתוסין להטעות את חכמים שכרו שני בני אדם בד' מאות זוז אחד משלנו ואחד משלהם שלהם העיד עדותו ויצא שלנו אמרו לו אמור כיצד ראית את הלבנה אמר להם עולה הייתי במעלה אדומים וראיתיו שהוא רבוץ בין ב' סלעים ראשו דומה לעגל אזניו דומין לגדי קרניו דומות לצבי וזנבו מונחת לו בין ירכותיו והצצתי בו ונרתעתי ונפלתי לאחורי ואם אין אתם מאמינים לי הרי מאתים זוז צרורין לי בסדיני
Initially they would accept testimony about the month from any person: Our sages taught: "What corruption did the Baytusim attempt to cause? One time, the Baytusim tried to mislead the chachamim. They hired two people with 400 zuz, one of ours (i.e. a follower of rabbinite Judaism) and one of theirs. Theirs gave his testimony and left. Ours came in to testify and they asked him, 'how did you see the moon?' He said to them, 'I was going up to Maale Adumim and I saw that it was crouching between two rocks. Its head looked like a calf, its ears were like a goat, its horns were like a deer, and its tail was resting between its thighs. I looked at it and became afraid and fell backwards. And if you don't believe me, behold, there are 200 zuz wrapped up in my clothes!'"
They try to bribe two people to give incorrect testimony to the beis din. Unbeknownst to them, one of the people they tried to bribe was a follower of the chachamim. When he comes to give his testimony, he gives a very embellished story of climbing up to Maale Adumim and seeing the moon and throws in "hey, by the way, check out these 200 zuz someone gave me." Clearly, he's trying to convey to the beis din that someone tried to bribe him and the continuation of the gemara makes it clear that the beis din understands his message. But what message was he conveying with his story of seeing the moon? Why couldn't he have simply said that the Baytusim tried to bribe him and really the moon had not been visible?