The following question Is there an explanation how abu Hurairah managed to narrate more than 5K hadith? is requesting for an explanation about how he was able to manage such a large number of narrations.
This question is the exact opposite. It's requesting for evidence if he narrated from untrustworthy sources or if such a number is not feasible.
I posed this answer to the linked question and it was deleted. And I noticed it can be rightfully posted here.
I researched this issue two years ago but I'm not a hadith or history scholar. My field is Islamic Philosophy and Theology so I don't pretend to have an "expert opinion" on this, I only write what I have learned from my own sources.
My first and primary source was the work by Shia Scholar, Allama Sharaf ad-Din about Abu Huraira which I recommend reading.
The point I wanted to highlight is that the numbers are only one issue. As far as I know Sunni scholars explain this oddity by relying on Abu Huraira's own claim that he had a very sharp memory and used to live in vicinity of the Holy Prophet (pbuh).
The latter justification doesn't explain why the (Sunni) hadith sources quote so little from Ali ibn Abi Talib who was by far the closest companion not just than Abu Huraira but any other companion, which is an important issue itself.
A more reasonable explanation than relying on Abu Huraira's own claims is that many of the hadiths he narrates are not witnessed by him but only transmitted by him without him mentioning that he's not the witness but only the transmitter. But this creates another issue that I will mention later.
More important than number of hadiths, is the hadiths he has narrated on non-existing virtues of Muawiya and some other Sahaba which are clearly forgeries, making him a very suspicious character overall. We also know about his ties with Umayyads and the Umayyads' need to elevate the rivals of Ali ibn Abi Talib which according to Sunni Imam Ahmad ibn Hanbal was done by forging haiths in favor of his rivals. One might argue these false hadiths might have been falsely attributed to Abu Huraira but they can also be easily explained by his close ties with Umayyads.
The other noteworthy point is his past lowly character as admitted by himself which could have made him manipulable by money and offer of political positions which we know he came to enjoy greatly under the Umayyads.
And with the usual Shia forensic tendencies, if you really trace this whole issue, it goes back all the way to decisions made by Abu Bakr and Omar to empower Umayyads against the Ansar and Banu Hashim, and whoever else would conform to their rule such as Abu Huraira. This is of course too controversial with Sunnis.
The issue of transmitting narrations from Ka'b ibn Ahbar is also a controversial thing and can't be corrected by a single hadith from Abd Allah ibn Umar specially considering how Ka'b was first empowered and allowed to transmit Israelities by his father, Umar, the second caliph. Having read the work by Wilfred Madelung, famous for confirming Shia views on early politics of Islam, it became a certain fact for me that many Sahaba used to narrate hadiths in ways that would bolster their own political agenda/position. Hence an objective hadith/history scholar must also take into account on how political bias of a Sahaba might have influenced the hadiths he narrated including their content, form and interpretation. As an evidence how Ka'b was controversial from the beginning, it is narrated that Ali ibn Abi Talib was outraged by Umar's consultations with Ka'b on religious issues.
Lastly, even if the numbers can be explained by his liberty at quoting anything he heard as attributed to the Prophet (pbuh) by other Sahaba, the question of motive writs large because Abu Huraira doesn't specify that he is not quoting the Prophet (pbuh) directly which is a sign that he wanted to pretend to be closer to the Prophet (pbuh) than he actually was. His liberty with quoting hadihts apparently once angered Umar on one occasion leading to his physical punishment.
Best regards
