I've designed battery chargers with LEDs the "wrong" way on the output to give a "battery connected wrong" indicator. There are all sorts of ways diodes and LEDs can be utilized, but I think we can all agree that the RS schematic is in error.
That works, but beware, newer InGaN used to make pure green, blue, violet, near UV and white, as well as some other colours with a phosphor, isn't as tolerant to reverse voltage, as old GaAsP and GaP, used to make red and orange. I haven't done any tests, but have found older red LEDs can tolerate reverse breakdown, whilst the newer ones are ruined. Data sheets typically specify maximum reverse voltages of 5V, but higher voltages can normally be tolerated.