I have a feeling we are talking about the same thing, but I'm not sure so...
A) If you have 12.4 kVA/unit and 20 units with no diversity, that's 248 kVA at 100%. However, you can then use the diversity factors in Section III, but I haven't had the chance to run up an example of this yet to see how it would turn out.
B) If you have 17.4 kVA/unit with 20 units and 38% diversity factor, that's 348 * 0.38 = 132 kVA
So in A above, this would use a centralized system with has no load diversity that can be applied, since the full load may be used from time to time. However, this single load is likely to be much less than the sum of the connected loads for the individual unit based heating and/or cooling, and likely to be roughly equal to those loads actually once 220.84 diversity is applied, as in
C) 12.4 kVA/unit on 20 units at a randomly chosen actual effective diversity of 40% (it will likely actually be 3 kVA + 35% of remaining on the lighting load calc which includes most receptacles, plus the diversity on all ranges) = 99.2 kVA and then if the central cooling/heating is roughly 35 kVA, it's a wash.
This is what I'm getting at. I understand the purpose behind the 220.84 requirements, but the reality is that once you go through the long version of the exercise in section III, the result is probably going to be exactly the same as if you just said "lets throw in 1500 VA dedicated to electric heat and then never put it in there". Which is probably why the AHJ signed off on that.
That's where the common sense and experience over strict code adherence likely comes into play....