Section 4.1 of the paper he linked discusses extensively the limitations of linear model interpretability. Here's an example:

"With respect to algorithmic transparency, [the claim that linear models are more interpretable] seems uncontroversial, but given high dimensional or heavily engineered features, linear models lose simulatability or decomposability, respectively."

Given how many interesting problems are high-dimensional or solved through heavy feature engineering, you must be lucky to live in the happy space where problems are either low-dimensional enough to not need heavy feature engineering or where the client is already familiar with the high-dimensional features you're going to limit the model to using.

- http://www.saramitchell.org/achen04.pdf

The functional mechanism of a regression has nearly nothing to do with whether the regression explains the phenomenon it’s being used to model or not.