it also says:
"The Apple-Authorized Service Provider or Apple Retail Store will provide you with your service options after assessing your adapter."
In my case the service option was always "buy a new charger". I would still go to Apple and ask - perhaps it has changed now. Anyway one could in principle buy a broken charger of the same time, in which the power cord is not damaged, and replace the power cord from the other charger. Will be much cheaper than buying a new charger. But it should be done in accordance to electronic safety standards and performed by someone who deal with such repairs professionally, say any TV repair place.
Aha and beware: there are $5 replacement cords avaiable in the internet. Those seem to circumvent some features of the one-wire protocol with which magsafe connector speaks to the Mac. I would not recommend using them. For example one that I have used does not admit the normally present one second delay between attaching the magsafe and switching on the power. This is dangerous as if you switch the magsafe slowly you may cause sparks and short circuits.