Most radio clocks work in much the same way as a standard quartz clock – the only difference being that they respond to a synchronisation signal (normally once a day), and adjust accordingly.
People incorrectly believe that these clocks are very accurate, but in reality you would achieve the same result, resetting a quartz clock once a day manually, to a time signal broadcast on your radio.
Tell your friend to move the clock to a location where it will receive a stronger signal e.g near a window. Otherwise to buy a standard quartz clock, these days most have an accuracy of better than 5 seconds a month – if your friend needs to know the time more accurately than that, they are very sad.