Firstly, pretty much by definition, every situation will be unique. Factors that you may deem insignificant and not worthy of mentioning may be crucial in diagnosing a condition. A trained doctor should be aware of these factors, and ask pertinent questions to consider these factors. People unaware of such confounding factors may just pattern-match on the information you have provided, and come to an erroneous conclusion.
The "facts referenced on a sheet of paper" are (ideally) distilled from well-designed studies appropriately carried out (double-blinding, suitable controls, adequate statistical power, etc). This is arguably better than the "raw, personal information" which represents a single datum, with no control whatsoever. Granted, studies may not exist for a large range of conditions, or may be performed poorly, etc. I would still be wary of testimonials by unqualified people, however.
Secondly, which is something of a rehashing of the first point, the people asking the questions may not know enough to ask the right questions. I've heard this commonly referred to in the CS world as an "XY problem"[1]. Paraphrased, "You've concluded your problem is X, and you want to know a treatment, Y. Instead of asking about X, you ask about Y".
This may involve providing incomplete medical history to answer a question, or not have access to various diagnostic equipment, etc.
Thirdly, how does it "[focus] on the key health topics"? It looks something not dissimilar to a stackexchange site, perhaps without the editing/metacommenting/badges, etc. I assume some moderation will be in place to select these key health topics, and perhaps eliminate the spam? The main forms of communication (towards answering a posed question) appear to be adding answers, or voting up others. I'm not sure that's a suitable model for health issues - you're either going to end up with people upvoting things that they can (however vaguely) relate to, or adding additional answers to espouse their personal pet theory, adding noise to the discussion. I'd therefore look to the SE sites for ideas, such as communal editing, etc, but I think a score/badge related system is inappropriate for this subject.
Finally, I'm not sure of the legal situation, but I can certainly imagine that actual medical professionals would avoid answering questions, due to concerns about liability and professional ethics issues. Much the same occurs around law-related topics (disclaimers abound: IANAL, IANYL, etc). Without that countering opinion, I fear it may drift into placebos, rainbows and unicorns territory. I couldn't say for certain that will be the case, but the first question I looked at, the answer pointed to a thread on "earthclinic", with a huge number of people suggesting various vitamins, supplements with little or no justification for their use.
I realise this post is excessively negative, but I am deeply dubious of the value of "crowdsourcing" for situations in which lives may be at risk, and people could waste time waiting for answers, instead of going to the doctor or emergency room.
Perhaps the most useful way I think it could be used is as a sanity-check for actual diagnoses or treatments. "My doctor thinks I have X, and has prescribed Y, but there is no sign of improvement, any other ideas?".
Even then, I think it's fairly common practice to ask your doctor to refer you for a professional second opinion, which would probably be more useful. Then again, a fresh and distinct pair of eyes could pick up something a hurried, "treat as the most common case first" doctor might miss, as indicated by your facebook/autoimmune link upthread.