Basil,
Simple. Because the usual simple boring government way of just sticking drives through industrial shredders would not sell newspapers.
So the Grauniad wanted to make a big show and dance, because quite honestly thats all the destruction of a couple of physical drives would be ... just one big show. GCHQ would be more interested in making sure things weren't hiding elsewhere on the Grauniad network and I suspect separate discussions were held with the Grauniad IT department over that.