Much of History is hearsay, you are corrrect. I have a degree in History and I know that the writings of Herodotus, Livy (Titus Livius, who I get my board name from), Plutarch and others are merely books of rumors and out and out fabrications. I don't rely on them to be truthful because they are stories passed down generations later. Most likely they contain a mix of truth and fiction.
The same goes with Hadith. The same goes with the Bible.
Scholars have had to debate which Hadith are authentic and which aren't, and even this science can easily get it wrong, as a true Hadith can be dismissed because the scholars didn't believe them enough. As I have already mentioned you also have different Muslims that believe different Hadith, which shows that part of this "science" is simply opinion.
So what percentage, roughly, of hadith were written down when they happened? Or when Muhammad was still alive?
i just wanted to address one point. there is NO difference of opinion "among Muslims!" Shiia use different hadeeth because they are misguided. Shiism is NOT, REPEAT NOT ISLAM! PERIOD!
peace