This seems like the dog version of the cat I had a long time ago who would jump in the sink and let the water run on the top of his head any time you turned it on.
I had a cat that would refuse to drink out of her water bowl and trained us all to turn on the sink when she was thirsty.
The problem was partially remedied when she got too old and lazy to jump up onto the counter. We got her an auto dispenser that keeps the bowl full, but she'd always dig water out onto the floor *I think* in the hopes that the new water would be colder. It took her several years to figure out that the water in the reservoir isn't any colder like the water from the tap.