I think you're misreading the article. Science is about theory and observation, with no presumption that the latter must fit the former.
As much as a physicist might hope to uncover a universal law that is simple enough for children to memorize yet subtle enough to warrant a lifetime of learning to fully understand, nature is perfectly content with fundamental parameters that settle into working values completely at random.
Fair enough. He was specifically speaking to 'naturalness' as technical designation in physics. I am getting a little more general.
The scientific method seeks to be entirely empirical - which makes sense for understanding what we can observe.
But what happens when what you are trying to understand is not observable? You fool yourself if you think you are being empirical when you are not. (His comment about moving the yardsticks applies here).
Any endeavor to understand the universe, especially origins, ends up involving philosophical presuppositions. Science aspires to avoid that, but can it?
As much as a physicist might hope to uncover a universal law that is simple enough for children to memorize yet subtle enough to warrant a lifetime of learning to fully understand, nature is perfectly content with fundamental parameters that settle into working values completely at random.