No one is saying its magic.
Engineers have told me there is no difference in safety between allowing a CNG tank in your car stored in your garage, and having a tank in your home. So if the government says it is safe enough to have in your car - where you drive around at high speeds on a highway, and then store it in your garage, it should be safe enough to put it underground and at a higher pressure. (Natural gas is safer than gasoline for driving!)
Compressors are expensive - but GE is now working on one for the home and they will bring the price way down. This is already happening.
Processing natural gas, is no where near the cost of refining oil, and no where near the environmental nightmare of building a refinery. To say those things are equivalent is totally wrong!
The concern is not the tank with no moving parts, but the compressor with a rotating seal.