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.