Is it possible that the very low resistance you measure between the base and emitter is due to the VR's being set to zero? I know there is still a 1ohm resistor that should be showing up, but maybe reverse the ohm meter leads so its not letting the B-E junction share some of the meter current.
If this explains away the low resistance, I think Bayou might be right about the bias diode's Vf.
If this explains away the low resistance, I think Bayou might be right about the bias diode's Vf.