I thought Bruce was helping me out here for a moment, but alas it's not so...
<start CS lesson>
In computer science, the testing of an algorithm has some trouble spots, which are usually tested at the various limits imposed on the function. For instance if the algorithm shouldn't get negative numbers nor should it get numbers over 100, then it gets tested to see how it functions with some negative numbers, zero, one, some more numbers mid range, 100, and some above 100. If the program functions properly with all these numbers, it's approved for use.
<end CS lesson>
For this particular issue, we don't have any problems when there is no risk of a column shift for cowering falling off the chart. The troublesome limits are at the edge of the chart where a unit would cower off the chart, as well as certain combinations of DRM with a 2 column shift for inexperienced.
This discussion is mostly limited to these limit tests, as for the other cases (higher FP or lower DRMs) both methods agree that a given attack will cause DM.
At it's core are the semantics and "spirit of the rules" interpretations.
Keep in mind that to remove the DM for breaking originally, in most cases a unit will be in rally terrain, someplace they wanted to be, that they think is safe. In order to get them to move out, they must be enticed by "enough FP" (or WP, ADJACENT enemy, etc.).
I see any 1 FP shot as incapable of inducing DM on an already broken unit, because of the possibility of cowering off the chart. (Same thing for inexperienced on the 1 or 2 column). This interpretation fits with the "enough FP" as a DM cause. Having the inexperienced units do the same for 1 or 2 FP columns is in keeping with their lower quality/poor equipment/lack of training/loss of NCO's/etc., whatever got them to Green or conscript status.
With an inexperienced unit firing, without the possibility of cowering off the chart, I see their inexperience shining through at the FP-DRM combination that has a DR two or three result (on the original column) the NMC result. Their 2 column shift means that the lower column used for cowering will result in a PTC or nothing, not enough for DM.
For all other cases, the Cowering column shift will result in the same NMC or better (worse for the target) result.
My interpretation of the "possibility of cowering" is that this clause is inculded to exempt the non-Cowering units from having to consider the column shift. Since there are 6 different DR combinations that Cower, you have to consult the lower column to see if there is still the possibility of a NMC result.
Boe's algorithm gives inexperienced units more capability then I think they deserve, and means that a 1fp attack on a unit in Woods (where the broken unit want's to take root) is enough to make them reconsider. To be firing on the 1 FP chart, most units would have to be at long range, or shooting in the advancing fire phase or both to get down to the 1 chart in the first place. You're already at a low volume of fire for whatever reason, so why is this enough to cause DM?