I realize that if somebody makes a transaction without any fees and there have not yet been any confirmations, then the transaction could be double spent by just spending the same inputs to a different address, but with a standard fee.
My question is, if somebody sends a transaction with a standard fee, and there have yet to be any confirmations, could that transaction be just as easily overridden by rewriting the transaction, but with a higher fee? If so, what would be the implications for a party that accepts zero confirmation transactions such as BitPay?