Each bitcoin has an attached chain of transactions. If it's a matter of public record that a certain address belonged to say, Stephen Colbert, then you can definitely brag that you own Colbert's bitcoin. (That he donated to the Libertarian Party or something.)

While it may be possible to value BitCoins that way, that's not the driving force behind current price tracking, any more than a 1933 double eagle or 1804 silver dollar affects the price of gold or silver.

I'm not saying BitCoins are currently used this way. It was just a thought experiment to prove they can acquire extra value from association with particular people or events. Just like other collectibles.

I don't think this is the case. My understanding is that wallets have transactions attached.

There is actually quite a bit of discussion into 'coloured' bitcoins, which would basically work exactly like that.