The article says that FM radios use very little battery, which is true. However, if in an emergency scenario (phone masts disabled through wind, flood, WWW3 EMP etc) one turns on Airplane Mode (without which a phone will burn through its battery looking for a non-existant signal) the FM radio is disabled - presumably because of the architecture of these Broadcom and Qualcomm chips. Without activating Airplane Mode, the phone will soon run out of battery anyway.
Tldr buy a Sansa Clip.