Is it true an ILS CAT IIIc can automatically taxi-in an aircraft?
There is no provision in the ILS system to provide for an auto-taxi or runway vacate. IIIc is just zero-zero and roll-out control, not auto-vacate as the linked AvWeb article seems to suggest. Its a logical extension of the FAA definition, however auto-taxi is not part of the CAT IIIc definition or system requirements. The only requirement is to get the aircraft on the runway and stopped.

FAA Circular 120.28C provides for the definition of a CAT IIIc approach:


  c. Category IIIc. A precision instrument approach and landing with no DH and no runway visual range limitation.


Right now there is no airport approved for IIIc approaches because the aircraft would just sit on the runway, it has no way of taxiing in. Until an augmentation system like GPS with WAAS or LAAS, or the "Ground-Based Augmentation System" is developed further, automatic taxi is not there.

There is no provision in the existing ILS signals that allow for an aircraft to vacate the runway. GPS is as close as you can get, but that may be unreliable especially with larger aircraft like the Airbus A380 that doesn't have much play on either side, so GPS accuracy will have to be augmented with something. Additionally a system will have to be in place to avoid aircraft from colliding on adjacent taxiways or to manage traffic in and around the gate. 

From a technical standpoint, this is a long way off, even with ground based radar systems, GBAS, and LAAS that are currently undergoing evaluation at several major airports world-wide. 

Also see this FAA Document 8900.1 and Order 8400.13D