In practice the answer is a massive “no” so far. Some of the least interpretable models I’ve had the misfortune to deal with in practice are misspecified linear regression models, especially when non-linearities in the true covariate relationships causes linear models to give wildly misleading statistical significance outputs and classical model fitting leads to estimating coefficients of the wrong sign.
Real interpretability is not a property of the mechanism of the model, but rather consistent understanding of the data generating process.
Unfortunately, people like to conflate the mechanism of the model for some notion of “explainability” because it’s politically convenient and susceptible to arguments from authority (if you control the subjective standards of “explainability”).
If your model does not adequately predict the data generating process, then your model absolutely does not explain it or articulate its inner working.
That's a very dynamicist viewpoint. I don't necessarily disagree.
However, in what sense to the prototypical deep learning models predict the data generating process?
I tend to agree that a lot of work with "interpretable" in the title is horseshit and misses the forest for the trees.
But it's also unclear to me how to get a decision tree to perform as well on image recognition tasks the same way that a CNN does. (Of course, as you mention, the CNN will likely face adversarial examples.)