Can energyplus model Airflow network with VAV supply fan?

The EnergyPlus documentation seems to say that an Airflow Network requires a constant volume supply fan.

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And yet, there is an example file (v8.8) with a variable air volume supply fan in an Airflow Network ..?

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Am I misreading the limitations, or is the documentation out of date?

Yes; the input/output documentation is out of date.

This section in the engineering reference describes the calculation procedure for AirflowNetwork with a Fan:VariableVolume and AirTerminal:SingleDuct:VAV:Reheat terminals.

You can also run the example file and verify variable airflow through the air system using the System Node Mass Flow Rate output variable as well as AirflowNetwork operation with the AFN Linkage Node 1 to Node 2 Volume Flow Rate variable.