Automatics can engine brake -- but in response to the person above who couldn't do it -- they typically do not exhibit that behavior in the default drive gear for fuel economy. (although some torque-converter automatics with inclination sensors
will automatically engine brake on downhill grades) Most torque-converter automatic transmission also have selectors for holding particular gears to allow the operator to command engine braking behavior.
As the other person mentioned, the quote you are citing means that you shouldn't spin the wheels of an automatic while the engine is not spinning. The input shaft of an automatic transmission typically drives the transmission's lubrication pump. If you spin the output shaft of a transmission of this design without spinning the input shaft, you are rotating the mechanism without lubrication.