Earlier quoted context omitted.
No you've bought .001 as you state yourself. The component parts of a bitcoin can be allocated. (I think the minimal is 1 "satoshi") 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.
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 amoun…
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.