I seem to recall a post here a while ago showing that dishwasher residue was genotoxic as well but can't find it atm.
[1] https://www.sciencedirect.com/science/article/pii/S009167492...
https://www.sciencedirect.com/science/article/pii/S009167492...
It's very, very definitely a thing.
I just put water in the rinse aid dispenser of my dishwasher.
Curious... Rinse cycle already uses plain water, so you are adding water to... water?
Looking at the back of a bottle of Finish Jet Dry (which I have refilled with water), the original stuff's first ingredient (after water) is "C 12-15 Alcohols Ethoxylated Propoxylated". These are nonionic surfactants, and are not what one normally means by "alcohol" (ethanol).
I can understand where the idea came from. Drinks like wine will exhibit sheeting on the sides of glasses too. The concentration of alcohol needed for that to happen is probably too high in a dishwasher, I'd imagine.