All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The narration which the questioner referred to is authentic and it is reported by Imaam Ahmad on the authority of Miqdaad Ibn Ma'd Yakrib (130/4) and it is reported by At-Tirmithi on the authority of Abu Raafi' (37/5) and reported by Abu Daawood (200/4), Ibn Maajah (6/1), Al-Bayhaqi, At-Tabaraani, Al-Haakim, Ash-Shafi'ee and Al-Humdiy, may Allaah have mercy upon all of them.
The wording of the narration reported by Ahmad is: "Beware! I have been given the Quran and the like of it with it; yet a time will come when a man replete on his couch will say: "Keep to the Quran; what you find in it to be permissible treat as permissible, and what you find in it to be prohibited treat as prohibited." Beware! The domestic ass and beasts of prey with fangs are not permissible to you…" Shu'ayb Al-Arna'oot said: "Its chain of narrators is authentic.'', and it is classified by Al-Albaani as authentic as well.
Abu Daawood reported the narration with a weak chain of narrators: "I swear by Allaah, I admonished, enjoined good and forbade evil, and it is like the Quran or more than it."
Therefore, the above narration is evidence that what the Prophet forbade is like what Allaah forbade in His Book, as the Messenger conveyed on behalf of Allaah.
The religious rulings are not only taken from the Quran only, rather they are taken from the Quran and the Sunnah, as clarified in the above narration. For instance, it is forbidden to eat a domestic ass, and it was prohibited by the Prophet similarly, beasts of prey with fangs are not permissible for us, and they were prohibited by the Prophet . Simultaneously marrying a woman and her maternal or paternal aunt is forbidden, and this was prohibited by the Prophet and there are many other examples like this (the prohibition was made by the prophet and not mentioned in the Quran).
A call to remove the Sunnah from legislation is a call to stray from religion.
For more benefit on the status of the Sunnah in Islam and legislation, please refer to Fataawa 91740 and 88197.
Allaah Knows best.