> Faced with this, one is better off putting extra cash into paying down the mortgage rather than in a savings account.
Cash poor means no easily accessible source of cash, it doesn't refer to the amount of money in your wallet. In your scenario you can access that cash again by jumping onto the banks website (or even visiting the bank) and moving it to your everyday account.
I used the term cash poor correctly for the scenario where you used your savings account to buy down the mortgage a bit. It's not quite so easy to increase the mortgage amount, it would depend on what the terms are if you are late or underpay a mortgage payment. If the terms are good, it is one way to recover the cash for an emergency.
Cash poor means no easily accessible source of cash, it doesn't refer to the amount of money in your wallet. In your scenario you can access that cash again by jumping onto the banks website (or even visiting the bank) and moving it to your everyday account.