Does every North Korean home have a radio ...
North Koreans in a changing media environment
Photo by AP photographer David Guttenfelder
A communal farm compound near Kaesong ...
Ordinary North Koreans rarely have access to electricity
Of course, this doesn't rule out battery-powered radios, but it does support the notion that some N Korean homes might be too poor to own their own radio.
... that can't be turned off?
A commenter to the linked photo
photo by Eric Lafforgue
well, In South Korea, those kind of speakers in apartment home only use for public announcement of apartment managing office. but in north korea, government took control to whole apartment....
So, to speculate a little: the pictured N korean home "radio" is probably also not a radio receiver but a loudspeaker for a communal system for relaying announcements. To be of value in emergencies, such loudspeaker units would probably not be equipped with an off-switch.
... that can't be retuned?
As pointed out by Oddthinking in a comment below:
All radio frequencies are fixed to the official broadcasting service channels and sealed. If the seal is found broken, the person involved is assumed to be guilty of listening to South Korean or other foreign broadcasting services and is treated as a political prisoner."
From Korea Institute for National Unification's White Paper on Human Rights in North Korea 2012
It is possible that a reporter has accidentally transformed "can't retune" to "can't turn off".
This might not apply to whatever report included the photo of a wall-mounted "radio" that lacks any obvious off-switch.