I went searching, because it does sound like quite the quotable claim. Almost everyone who talks about the efficiency of handwashing seems ultimately to be referencing the same paper[1], although virtually nobody cites it.

The peak of the distribution of water usage is in the 40-50 litre range, however a nontrivial number of people use an absolutely enormous amount of water. The paper gives some observations about different approaches to washing, although it doesn't describe them systematically.

[1] https://www.tempurl4.uni-bonn.de/forschung/haushaltstechnik/...