I think dclowd9901 was getting at a different question, which I'll present by analogy:
I incorporate with 1,000,000,000 shares of stock. I sell 20 shares of stock to my good friend for $50. Is my company now worth 2.5 billion dollars?
The answer to this worry is that the value of the good (bitcoins or stock shares, or anything else) is reliable in proportion to the total trading volume, not in proportion to the amount one person typically buys in a single transaction, or even the amount that one eccentric rich guy bought that one time when he was drunk.
Thank you; you explained this much much better than I did.
But your answer, I don't think is sufficient. Just because total trading volume supports the figure doesn't mean that it's valid. If I've invested a small amount of money into the currency (as I suspect most of its buyers have), I've essentially bought into an insane price for little or no "skin". In other words, the price could be high simply because there's no risk to it being that high for most of its investors.
By "total trading volume" I meant to total across buyers and sellers, not to total across history.
Going back to the analogy, suppose I incorporate with 1,000,000,000 shares of stock and sell 20 shares to my friend for $50. He forgets about them, because after all the whole thing was just a joke.
My company has a market capitalization of $2.5 billion, of which I own $2,499,999,950. That paper wealth is worthless, because the daily (or whatever) trading volume of stock in the company is $0, suggesting that if I tried to realize my immense wealth, I wouldn't be able to.
Suppose instead that I sold 500,000 shares to my friends for $50 (total - 10,000 shares to the dollar), and that they sold the shares on to the public, and that now 10,000 shares trade per day at $2.50 per share.
My company has the same market capitalization of $2.5 billion. I own $2,498,750,000 of that (plus $50 of cash!) -- not as much as I had in the first example, but still pretty good. Just as in the first example, the daily trading volume suggests that this wealth is mostly illusory -- the tiny $25k / day market will be quickly overwhelmed if I try to sell $1 million worth of stock, and the trading price will plummet. However, unlike in the first example, my wealth is not entirely illusory. If I try to pick up an extra $5,000, I'll probably have to sell more than 2,000 shares of stock, but the trading volume can support that amount.
As long as there is active trading at a price, that price is real. There is no such concept as trading enough of a bitcoin for the price of "a bitcoin" to be "real"; what matters is whether you're trading enough of the market to move the price single-handedly. If the amount that you want to trade is much less than trading volume, you can more or less rely on the market price. If you want to trade an amount which is noticeable relative to trading volume, you're going to change the market price.
Put another way, if bitcoin trade volume is 100,000 bitcoins per day, you can sell one bitcoin at the market price even if nobody ever buys or sells more than .00001 bitcoin in a single transaction.
It's a bit like buying one pen out of a very large pack of pens. You don't own the pack if you only buy one.