Oz, et al, even if not intelligent, EGPWS has excellent logic and when heeded has immense capability to save lives.
If the reported EGPWS alert was ‘Sink Rate’ (which I am unable to confirm) then this should have been generated by mode 1 which uses aircraft vertical speed vs Rad Alt. The VS required would appear to be very high for the scenarios surmised so far.
However, if the alert was ‘Don’t Sink’ then this might have been generated by mode 3, but the description of this suggests a dependency on gear and flap switching to determine a difference between after take-off and go around. Although the latter function might apply in this accident, the reported gear and flap position suggests not.