Complete bullshit.
ABS is controlled by its own separate control unit, which is attached directly to the hydraulic unit containing a hydraulic pump and the valves that apply or release brake pressure in a controlled fashion.
The ABS function is completely self-contained. The wheel speed sensors are connected directly to the ABS control unit as are the brake pressure senders, the yaw rate, lateral acceleration and steering angle senders and the TCS/ESP on-off switch.
The brake pedal has no electrical connection to the ABS unit, the unit reacts to wheel speed and brake pressure inputs for ABS, EDL and TCS, and adds the ESP sensors (yaw, lateral acceleration, steering angle) for ESP control.
The wheel sensors are just sensors and have no independent processing power or attached processors. The accelerometers may have some preprocessing at the sensor head.