Complex, lengthy topic of tone reproduction. There are lots of variables at work here. Film speed, the meter, flare in the scene, film curve, paper curve and on and on. And there are different interpretations of what "Zone" actually means when it comes to the exposure placement versus the negative density versus the paper tone (reflection density). Remember that just because you expose two stops below metered, doesn't mean the resulting negative density will produce a Zone III tone on the paper.

I suppose a simplistic answer in this case is to give more exposure to the film (ie use a lower exposure index).