Imam Aḥmad could have dismissed that on the grounds that no established report exists from those who relate that Ibn ʿArʿarah heard it from him; there was no need to state explicitly that he was lying. Reflect on this.
In sum, the hadith is authentic in any case, whether Ibn ʿArʿarah’s having heard it from Muʿādh is established or not. In the former case, this is clear, given Ibn ʿArʿarah’s trustworthiness and precise retention. In the latter case, at most his narration would be a sound wijādah—a transmission based on a written source—from Muʿādh’s book, which Muʿādh had personally handed over to him. It is therefore among the strongest forms of such written transmission, accompanied by the shaykh’s handing over of the book. And with Allah lies success.
What further strengthens the hadith is that it has a strong mursal corroborating report. Al-Bayhaqī said immediately afterward, indicating that it strengthens the hadith: “Al-Thawrī narrated in al-Jāmiʿ from Ibn Ṭāwūs, from Ṭāwūs, that the Prophet, blessings and peace be upon him, would depart every night—that is, on the nights at Minā.”
805 — “During the time of the Messenger of Allah, blessings and peace be upon him, we used to take provisions of the meat of the sacrificial animals to Medina.”
Imam Aḥmad recorded it (3/309): Sufyān reported to us, from ʿAmr, from ʿAṭāʾ, from Jābir, who mentioned it. Through this same chain, Ibn Abī Shaybah also recorded it in al-Muṣannaf (4/57), and Muslim recorded it in his Ṣaḥīḥ (6/81) through Ibn Abī Shaybah. Al-Bukhārī (6/239, Istanbul) and al-Bayhaqī (9/291) also recorded it through other chains from Sufyān ibn ʿUyaynah, with the same wording. Shuʿbah likewise narrated it from ʿAmr ibn Dīnār. It was recorded by al-Dārimī (2/80) and Aḥmad (3/368).
Ibn Jurayj also followed ʿAmr and said: ʿAṭāʾ reported to us, with the wording: “We would not eat the meat of our sacrificial camels for more than three days at Minā, until the Messenger of Allah, blessings and peace be upon him, granted us permission and said: ‘Eat and take provisions.’ I said to ʿAṭāʾ: ‘Did Jābir say, “until we came to Medina”?’ He replied: ‘Yes.’”