Like transponders, can flight recorders be turned off?
There is no switch for the FDR, but there is a circuit breaker and by pulling this you are removing aircraft power from the FDR.  However, this does not mean you are necessarily turning it off, as some FDR can be equipped with an internal power supply as a backup to aircraft power.  

The quote in the question (bolded emphasis mine):


  You also cannot turn off the black box, as it runs throughout the flight, recording every 30 to 60 seconds.


is a case of an "expert" or journalist confusing the lack of an on/off switch as an inability to turn something off.  As you'll find many examples of in the media, they don't always get it right.  The circuit breaker may not be a true on/off switch, but pulling it does accomplish de-powering (assuming no internal power supply) and thus turning off the FDR.