All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The authenticity of this addition to Ibn Abi Haatim in the mentioned example cannot be decisively stated. It is known that there are five conditions for a particular hadeeth to be classified as authentic. Three of these conditions are related to the chain of narrators, and two are related to the text.
The three conditions related to the chain of narrators are the following:
1) Connectedness (i.e. every narrator must have met his predecessor, who narrated it to him in an uninterrupted chain all the way back to the Prophet, sallallaahu ‘alayhi wa sallam).
2) Trustworthiness.
3) Precision of memorization.
The two conditions related to the text are the following:
4) The absence of Shuthooth (which means that the hadeeth is narrated by a trustworthy narrator but differs from the narration of other trustworthy narrators) in the text .
5) The absence of ʻIllah (subtle hidden defects identified by versed Hadeeth scholars and critics, deeming the hadeeth inauthentic while on the surface it may seem authentic) in the text.
Hence, if the Hadeeth scholar does not declare a particular part in a hadeeth authentic, it is possible that it may be classified as an aspect of Shuthooth or ʻIllah in that hadeeth according to his opinion, even if he declares the chain of narrators of a part of the hadeeth authentic or classified this same chain of narrators in other ahaadeeth as authentic.
Ibn Al-Qayyim wrote, "It is known that the authenticity of the chain of narrators is one of the conditions of the authenticity of a hadeeth, but it is not the only condition. A hadeeth is declared authentic when a set of conditions are met, including the following: an authentic chain of narrators, absence of ʻIllah, absence of Shuthooth and Nakaarah (which means that a narration reported by a weak narrator goes against another authentic hadeeth)."
Allah knows best.