The S3 does not have an induction coil and regulator circuit built into the phone across the charging socket/battery terminals with which one can induce a current electromagnetically. Wireless chargers by definition do not rely on direct metal contact outside the phone case to create a voltage across the battery terminals. In fact, a metal phone case is only serves to block the field generated by the induction coil in the charging mat/pad.
The charging pad works by creating a transformer with one coil in the pad and the other in the phone attached to the battery. Since there is no coil in the S3, a coil has to be added into the phone via a new outer battery case. The antennas in the phone are not sufficient to power the device, merely to transmit radio signals for communication--EDIT (Even though the NFC antenna is built into the battery).
While this transformer setup is referred to as "Near Field", the relationship to the NFC Near Field Communication (13.56MHz) standard used for communication is only one of proximity--over short distances (<20cm).