Did Imam Bukhari and Imam Muslim ever believe in Sahih hadiths that they did not put in their compilations? If they did, then why didn't they include them in their compilations?
Yes! They did believe in some reliable hadith that they did not include in their compilations.
"What I have included in my book "Al-Jama'i al-Sahih" is correct, but there are many reliable hadiths that I did not quote in order to make my book longer."
Muslim bin Hajjaj Qashiri says:
"I have not included all the reliable hadiths in the "Sahih" book, but I have tried to mention only the hadiths that are unanimous."
Reference by hawzah.net