That's simply not what I said. The confounding factor isn't hand washing (though that also makes it impossible "model the effectiveness of respiratory masks" as

That's simply not what I said. The confounding factor isn't hand washing (though that also makes it impossible "model the effectiveness of respiratory masks" as the title says), it's that it's comparing one department to other departments, and those departments surely differ by more than just hand washing and face masks. Infectious disease specialists were trained differently, do different procedures, etc. They see patients with different symptoms and at different stages of their disease. Essentially the way to treat this is not a study of N doctors but a study of only n departments, which turns it more into an anecdote - albeit a compelling one.