for example, many of us are aware of the "fact" that the Prophet consummated his marriage with Aisha when she was 6 years old. however, is there any proof of that in the Quran, the only infallible book on earth? sure there is proof in the hadith, but what kind of proof? all you have is a book written, nay compiled, by bukhari, or tirmidhi, or abu dawood which says that so and so said that such and such happened. since when is hearsay as good as gold?
Asad bhai, I will have to read your post again to fully understand what you want to say. I have just skimmed it. From that, purpose of the example that you have used in your post is not clear to me. Ummul Mumineen Aisha's (R) age of marriage is a fact, it doesn't have to be hadeeth. Because what is hadeeth? It has to be the word of the holy prophet, or his deed or his silent support to any deed. The above example din't fall in this catagory, so of course this is not a hadeeth.
Also, the hadeeths are memorised just like Quran. Until the invention of paper and printing, hadeeth was preserved the the way Quran was preserved-memorising. While memorising, and reporting hadeeths, sahabae keram mentioned not only the exact words of the prophet, but also exactly from whom they have heard or memorised the hdeeth.