This is not correct, for Ibn Abi Layla—despite the weakness mentioned above—was not included in the Sahih. Perhaps the two of them mistook him for Abd al-Rahman ibn Abi Layla, Muhammad’s father; he is the one whose reports were included in the two Sahihs, but Muhammad is not he. Take note.
However, it may be said that the hadith is good by virtue of its corroborating report from Ibn Abbas, attributed to the Prophet, may Allah’s peace and blessings be upon him: “Let every man eat from his sacrificial animal.”
Al-Tabarani recorded it in al-Mu‘jam al-Kabir (3/174/1), and Abu Nu‘aym, through him, in al-Hilyah (4/362), by way of Abd Allah ibn Khirash, from al-Awwam ibn Hawshab, from Abd Allah ibn Abi al-Hudhayl, from Ibn Abbas, attributed to the Prophet. Abu Nu‘aym said:
“It is singular among the reports of Abd Allah; we have recorded it only through this chain of transmission.”
I say: It is very weak, for there is agreement on declaring Abd Allah ibn Khirash weak. Al-Saji said:
“He is very weak in hadith, of no account; he used to fabricate hadith.”
Al-Bukhari said something similar:
“His hadith are rejected.”
In short, it is severely weak and therefore unsuitable as corroboration, so the hadith remains weak. And Allah knows best.
Then I found something that strengthens it: the report of Sharik, from Abd al-Rahman ibn Abi Sa‘id al-Khudri, from his father and Qatadah, that the Messenger of Allah, may Allah’s peace and blessings be upon him, said:
“Eat the meat of the sacrificial animals and store some of it.”
Ahmad recorded it (3/48).