Well, the benifit of your friends suggestion would be that if you weren't able to regularly afford to pay the monthly payments of a 21 year mortgage, then remortgageing to a 30 year term would decrease the monthly payments. The total amount payable (the amount you would have paid by the end of the mortgage) would increase quite a lot by doing this.
The "trick" your friend means is, that you have a lower regular montly payments. If you can afford to "overpay" monthly, then you will reduce the total amount payable. Like someone said earlier, if you "overpay" by the saving of the monthly amount you'd probably pay it off in 21 years anyway.
It gives you the flexability of overpaying when you can afford to.
I'm assuming it's a repayment mortgage, and that you'll be allowed to do overpayments without charge, and the rates are the same.
Can someone confirm this is correct?