The setup you describe is for proving (with some statistical certainty) a certain causal relationship.

But the author doesn't want to prove it. It has already been proven experimentally. What he said is that he can tell us from his own experience. You don't need a controlled study for that.

I can tell from experience that a certain vitamin X deficiency can be very bad (e.g. because I had it, my doctor verified it, and I got very sick and had Y symptoms) without needing to prove that vitamin X causes Y if it's already proven.

Which is the same case with vitamin D. The parent didn't say he'll prove something novel, just that they'll verify it from experience.

Note that verification from experience is still very useful, even when something isn't proven. It's not as rigorous as science, but it's still very useful, can be life-saving, and it's how civilisation advanced for 1000s of years before we got "controlled studies". People already knew from experience not to eat X or Y plant for example (e.g. poisonous), without official studies and control groups.

People should still be required to be able to make deductions and learn from experience at this level before they offload everything to scientists.