My understanding is that the compulsory DASK insurance will cover you up to a certain financial limit, which is probably enough for a very, very basic 'rustic' build out in the country (4 walls and tin roof!). It will not pay enough to rebuild a place to a reasonable standard. The price of the DASK is dependant on the building construction type and the floor space.
If you take out an insurance policy with any insurer, such as Intasure or a Turkish company, to cover you for say £60,000, in the event of an earthquake claim they will pay you £60,000 less the amount you should get back from your DASK insurance (lets say £5000 for this example). If you don't have DASK insurance you will be short of whatever amount they would have paid so in this example the insurance company would only pay you £55,000.
Hope this helps.