Like others have pointed, you have made a mistake in your computation. The currents that are required are only of hundreds of amps and the latest chargers can provide up to 1000 A.

Also like others have said, it does not matter how fast you charge a car, the total energy consumption is the same, so fast chargers do not require changes in the power supply of a charging station.

The fast chargers that enable this full charging in a few minutes have their own internal batteries, to enable them to pull only the average power from the electrical grid, not the peak power.

The new fast chargers that can achieve the times reported in TFA use a somewhat higher voltage than the older chargers, of 1000 V, to reduce the current.