The author couldn't find a purported willow text in the ancient Egyptian Ebers papyrus that was quoted by John Mann, so he threw his hands in the air and moved on.
But Mann made a mistake. The book he was likely quoting from, 'Science and Secrets of Early Medicine' by Jurgen Thorwald (which, to be fair, is not referenced at all by Mann) does mention the Ebers papyrus in the paragraph after the quote (on pp. 57-8 for people playing along at home) but the willow quote itself in the paragraph before turns out to be from the Edwin Smith Papyrus, Case 41 to be exact. It can be read here:
https://archive.org/details/oip3_20220624/page/374/
So that quoted willow did exist in ancient Egypt.
The commentary on the translation also illustrates the pitfalls of learning about ancient medicine from medical treatises of the time, discussing the word ḏrḏ: "The rendering “leaves” is not wholly certain; the word might possibly mean “bark” (cortex), and indeed in the case of willow, the bark is medicinally more efficacious than the leaves."
If you use modern medical knowledge to inform the translation (and interpret the phrase "the feathers of birds and the ḏrḏr.w of trees" elsewhere as referring to how trees are covered in bark just as birds are covered in feathers; see commentary on this dictionary entry: https://tla.digital/lemma/185150 ) you potentially get a more accurate translation, but you cannot treat it as independent evidence for the use of willow bark as opposed to willow leaves. Hopefully at least the identity of the willow tree has been established in a less circular manner.