@bythewell - I'm not sure they completely understand why the willow water works, or even why the acne treatments work, although you're right to say that the cells in question are very different.
This has made me realize why willows are such a pest in some areas. They tend to grow too thickly around waterways and clog them up, affecting both the natural environment and also the humans who are using the waterway for whatever reason.
They must spread really quickly if a single branch can grow a whole new willow tree without any problems.
They'd be difficult to get rid of permanently as well, since if you missed any branches they would quickly grow into a new set of problems.
I will have to remember the trick of using willow water as a rooting solution though.