Decision trees are not a statistical model. The learning method is statistical, if you will, but the model itself is a disjunction of conjunctions- a symbolic model (and more specifically, a propositional logic theory).

Decision Trees are in fact an example of the early years of machine learning where the trend was towards algorithms and techniques that learned symbolic theories. I believe the effort was driven by the realisation that expert systems had a certain problem with knowlege acquisition [1] which drove people to try and learn production rules from data.

I digress- I mean to say that decision trees are explainable because their models are not statistical.

To be honest, I don't know much about additive models.

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[1] https://en.wikipedia.org/wiki/Knowledge_acquisition