Both views feel extreme to me. When I was single, sometimes I used the dishwasher, and sometimes I washed by hand. In either case I wasn't wasting water, because I didn't run the dishwasher until it was full, which was roughly biweekly.
When washing by hand, I did what you imply you do, which is use much, much less than bowlfulls of water for my meal. I get what parent is saying though, because of the numerous roommates I'd had while single, some of them would use gallons of water to wash a single meals worth of dishes, i.e. the plate, cutlery, and maybe a cup. Much more if they had cooked their meal instead of microwaved it