With its insulated walls and rubber door seals, a refrigerator is the most soundproof box commonly found in ordinary living spaces. If it's running, even better, it provides white noise. If one was worried about listening devices, then a fridge would be a reasonable and available place to stash them. And Snowden has alleged the NSA can do lots of things even with a phone that's turned off.

Minor update: Out of curiosity, I put my phone in the fridge, and later in the freezer, with batteries still inserted. In both cases I was able to call it quite easily - the refrigerator did not act as a Faraday cage - but the ringtone volume was noticeably subdued. So I do think the fridge in the quoted story was a soundproofing issue, not a Faraday Cage as has been suggested.

I know it's just an experiment of one, but it was a fun experiment :)

Even more minor update: I was curious and checked... my microwave, which is a Faraday Cage, doesn't block cell signals either (good explanation here).