I am not sure where this opinion is coming from, and I do not claim that it never existed, but I have not come across it. On the contrary, Ahmad ibn 'Abdul-Wahhāb Ash-Shanqīti in his book Khabar al-Wāhid. pp. 249 quoted Ar-Risāla by Imam Ash-Shafi'i with him saying that there is no known disagreement among Muslim jurists that ahād hadiths are acceptable for jurisprudence, then he added he did not deny or reject any of them [the companions], as this would have reached us as did his teachings.
As examples of Ash-Sahfi'i using hadiths narrated by 'Amr ibn al-'Ās, refer to one of his multiple debates, with this one being documented in both Al-Umm 7/99 and Ar-Risāla al-Jadīda 2/493-495, Imam Ash-Shafi'i proved ijithād by referring an ahād hadith by 'Amr ibn al-'Ās, which he also documented in his Musnad, pp. 244. Note that 'Amr ibn al-'Ās did not narrate a lot of hadiths (fewer than 40, and even fewer that touched jurisprudence).
As examples of what Imam Ash-Sahfi'i said about Mu'awiyah is what he mentioned in his Musnad, pp. 86 about the story of Kuraib [ibn Abi Muslim] when he saw Mu'awiyah pray the nafl of the 'ishā' prayer as one rak'ah only. Kuraib informed Ibn 'Abbās, who told him that there is no one more knowledgeable among them than Mu'awiyah. The testimony of one the Muslims greatest scholars of all time, Ibn 'Abbās, is a credit to Mu'awiyah. Imam Ash-Sahfi'i documented it in his Musnad obviously because he trusted it. The examples are numerous, but here are two more examples. In Al-Umm 1/108, Imam Ash-Sahfi'i quoted Mu'awiyah about what to say at the time of adhān as attributed to the Prophet. Again, in Al-Umm 5/125, he narrated a story where Mu'awiyah had a different opinion about how to handle the marriage dispute of 'Aqīl ibn Abi Tālib and Fātima bint 'Utba ibn Rabī'a — in contrast to the opinion of Ibn 'Abbās — and how Mu'awiyah's opinion was right.
The confusion about the acceptance of what Imam Ash-Shafi'i said in his old books (Arabic: أقواله في القديم) versus his new books (Arabic: أقواله في الجديد), as documented by scholars of fundamentals of jurisprudence about proof by a ruling of a companion (i.e., a hadith that is mawqūf on the companion, in the companion's own words). There are three rumors floating around:
- He used them as proof in his old books, but not his new books.
- He used them as proof in his new books, but not his old books.
- He neither used them as proof in his new books nor his old books.
The closest to reality is option 2. This is not in relation to their narration of hadiths but in relation to their ijtihād or their qiyās.
In his old book, Ar-Risāla al-Baghdādiyya (see As-Sunnan al-Kubra, pp. 109), he said — in disagreement with Imam Malik — that if two companions disagreed about a matter, then one needs to examine their opinions in light of the Qur'an and the Sunnah to see who agreed with which companion. If there is no evidence from the Qur'an or the Sunnah, then the sayings of Abi Bakr, 'Umar, and 'Uthman are taken as reference. If there is no tradition through Abi Bakr, 'Umar, or 'Uthman, then it is the ijmā' (consensus) of the jurists of his time or the preceding times (before 200 A.H.). If any of the four previous methods fail, then it is a matter of ijtihād.
In his later years, in a debate with Mohammad bin Al-Hassan (see Adāb Ash-Sahfi'i, pp. 119-120), he debated that after the Qur'an and the Sunnah, he would revert to qiyās based on the sayings of the companions. He changed his view after his trip to Egypt as was documented in his book Al-Umm 2/31 saying that the sayings of the companions are his fourth source (Arabic: قُلْت إنَّمَا الْحُجَّةُ فِي كِتَابٍ، أَوْ سُنَّةٍ، أَوْ أَثَرٍ عَنْ بَعْضِ أَصْحَابِ النَّبِيِّ - صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ - أَوْ قَوْلِ عَامَّةِ الْمُسْلِمِينَ لَمْ يَخْتَلِفُوا فِيهِ، أَوْ قِيَاسٍ دَاخِلٍ فِي مَعْنَى بَعْضِ هَذَا ثُمَّ أَنْتَ تُخَالِفُ بَعْضَ مَا رَوَيْت عَنْ هَؤُلَاءِ). In his new book, Ar-Risāla al-Jadīda 2/596, he said after the Qur'an and the Sunnah and ijmā', if the sayings of the companions, even if it is one of them only, he would take it, or he would do qiyās.
In conclusion, in his earlier years, Imam Ash-Shafi'i accepted the hadiths (including ahād) from all companions, and did not doubt them, but did not use their ijtihād as proof. In later years,m he continued to accept the hadiths (including ahād) from all companions and added their ijtihād as a fourth source of jurisprudence.