Scenario: You can't wait around for one or several confirmation blocks. Instead, you receive the transaction, broadcast it to nodes you know and wait for a couple of seconds to see if you notice any double-spend attempts. If not, you accept the payment right away.
In the current Bitcoin scheme, one can't accept transactions until it has been incorporated into a block. Suppose two transactions "spending the same coins" enter the network at different points. On average, half the network will have one transaction and half the other. The only way out of this deadlock is which happens to make it into a block first. So you can see that the race across the network is unimportant but the race to get into a block is the deciding factor.
Hal's attack above would yield a reliable income.
ByteCoin