Does what al-Bukhari and Muslim agree on yield certainty of its soundness?

Ibn al-Salah divides the sound hadith into seven classes:

1. what al-Bukhari and Muslim both report;
2. what al-Bukhari alone reports;
3. what Muslim alone reports;
4. what meets the conditions of both but neither reports;
5. what meets al-Bukhari's conditions;
6. what meets Muslim's conditions;
7. what others hold sound but meets the conditions of neither.

The highest is the first, of which hadith scholars say "sound, agreed upon". They mean the agreement of al-Bukhari and Muslim, not of the community. Yet the community's agreement follows from it, because the community received what the two agreed on with acceptance. ^{1 2}

Ibn al-Salah describes the view he rejects as that of those who argued as follows: a hadith in itself yields only probability; the community accepted these reports only because it must act on probability; and probability can err. ²