[resf]

> As I understand it, bitcoin doesn't track coins so much as it tracks the funds associated with account numbers.

It's actually the opposite. The blockchain does track coins, but not accounts or account numbers. Rather, each transaction involves "scripts" which specify some conditions with which coins can be used as inputs to another transaction.

In a normal transaction, one key can spend the coins, but e.g. it is possible to send coins to a script that is impossible to satisfy, therefore the coins are unspendable, yet don't exist in an 'account' at all.