@barefootstache Honestly, this is just hair splitting and a hefty dose of recency bias. Salicyclic acid has been used since ancient Sumer, even though the effects were unpredictable due to variable dosing and personal acid sensitivity. Surprise surprise, you'll get the same variable effects if you give a person a random amount of ANY pharmacological compound; that doesn't mean the compound isn't effective.
Additionally, the personal sensitivity to the original compound was not due to the (likely more biologically active) salicyclic moiety, but the acidic one. Hence, by reducing the acidity of the medicine, and replacing the acid with an acetyl moiety instead, it improved the medicinal properties of an ALREADY medicinal compound.
This replacement can occur within a single esterification step from the salicylic acid which can be directly extracted from plants. Thus, considering the historical use of salicylic acid, and this being only a minor sidechain modification of a millennia old drug, it's not unreasonable to claim it's derived from willow extract, because it literally *can* be derived from it.
Of course we can control dosing better with modern isolation, titration, and gravimetry techniques, and of course modern chemistry provides a load indispensably useful solutions to age old problems. However, whether or not the compound is derived from industrial waste or willow bark, the inspiration to investigate this avenue came from early medicinal wisdom, which I think is an incredible legacy for our ancient ancestors to leave us.