[SODaniel]

Transaction records? Yes. Tied to a physical person? No. There is as far as I understand nothing hindering private trades among owners, making 'rigging' entirely possible (I may be wrong).

[mikegioia]

They're tied to a wallet ID which is unique.

Also, of course nothing is hindering private trades among bitcoins. Do you understand that BTC is a currency and not a stock exchange?