The first is that those who attribute it to the Prophet are trustworthy; they are both more numerous and more reliable.

The second is that the compiler of the Sahih chose the version that attributes it to the Prophet in his book.

I then found a corroborating narration for the hadith:

Ibn ‘Asakir narrated it (10/77) through Juwaybir, from al-Dahhak, from Ibn ‘Abbas, attributed to the Prophet ... and mentioned it with the same meaning.

I say: Juwaybir is one of the well-known exegetes whose narrations are abandoned; he is therefore very weak. *

3614— “While I was drawing water from a well, Abu Bakr and ‘Umar came to me. Abu Bakr took the bucket and drew one or two buckets, though there was some weakness in his drawing; may Allah forgive him. Then Ibn al-Khattab took it from Abu Bakr’s hand, and it became a large bucket in his hand. I never saw any man among the people perform as he did. He continued drawing until the people had watered their camels to their fill.”

It has been narrated from Ibn ‘Umar, Abu Hurayrah, and Abu al-Tufayl. As for the hadith of Ibn ‘Umar, two narrators reported it from him. The first of them was Salim, his son:

Al-Bukhari narrated it in (3633, 3682, and 7020), Muslim (7/113), al-Tirmidhi (2289), al-Nasa’i in al-Kubra (7636), Ahmad in his Musnad (2/28 and 39) and in al-Fada’il (224), Ibn Abi Shaybah (11/62 and 12/21), al-Bayhaqi (8/154), Abu Ya‘la (5514 and 5524), al-Tabarani in al-Mu‘jam al-Kabir (13177), and Ibn Abi ‘Asim (1456), through two routes from Salim, from him, with this report.