Isn't that a bit of a contradiction? If the base station either doesn't use or has batteries which aren't rechargeable, then the handsets won't continue to "work just fine" if the batts run out, will they?!
No contradiction at all.
The handsets work fine. Their display works. Their keypad works. Their RF section works. They work just fine. Without a working base station they're unusable (except as paperweights) but they do work.
I've upvoted you anyway for being a pedant. :)