I'm skeptical of this dubious assertion, but I will give it the benefit of my doubt. (Though I really doubt Aristotle had access to a refrigerator) What's more, I will even offer a third hypothesis as to why this might be true.
The heat of fusion for water is 334 J/g. That means for every gram of solid water at 0 degrees Celcius to be turned into liquid water at 0 degrees Celcius (or vice versa) 334 Joules of energy must be absorbed (or radiated) by the water.
So the winner of the race between the hot water and the cold water to the solid state probably depends on the temperature of the hot and cold water. The hot water will be better at melting the surrounding ice. But melting the surrounding ice will require 334 extra Joules of energy that comes right out of the hot water just to get the ice to cross from being solid to being liquid. That might just be enough to drop the temperature of the hot water below the temperature of the water which is considered "cold", so thus the hot water leapfrogs ahead of the cold water in the race to the solid state.
Another factor, it might be only the hot water at the edges of the ice cube tray that experience this benefit of losing the extra 334 Joules/gram of melted refrigerator frost. But, they might form seed crystals of ice sooner, and thus precipitate the freezing of the rest of the water in the ice tray.
I'm not a chemist though, so take all this with a several moles of NaCl, as I suspect that my hypothesis, full of scientific jargon though it may be, is a load of crap.
After thinking about it a bit more, (and reading what's below), of course my hypothesis is a load of crap. BTW, I also tried this with two cups of water (not ice cubes), and when I checked back later, both were frozen solid, so my empirical results are that they both freeze at the same speed. Which is also a load of crap. I always hated chemistry. (Yeah, this probably doesn't count as chemistry, I know.)