Now, I don’t know about the whole “hot water freezes faster” thing, but I do know this: hot water produces a better ice cube. As in all things, patience is a virtue, and if you are in a hurry and need your ice 15 minutes faster, then go with cold water and a lessor cube. However, if you are interested in obtaining cubes that are not cracked and falling to pieces, always start with hot water. What I have found is, cubes made from hot water, release from the trey more easily.
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I’ll bet it’s the fact that hot water has more time to sit around so that air bubbles and dissolved gasses leave (a faucet introduces a lot of those). It could also be that cold water forms an ice skin on the surface which is broken (repeatedly) as the water expands during freezing, while hot water just freezes at the walls. The pent-up pressure might also be a reason cold-water cubes are harder to release.
I was thinking it might be more interesting to use sun-warmed (say 80 degF), and cellar-temp (say 55 degF) waters and see what froze first. I mean, clearly if you cool the water all the way down to 38 deg F then pop it in the freezer, of course it will freeze faster than that at 125. Or even try 125 and 55.
The effect is well known, having been referenced by Aristotle “The fact that water has previously been warmed contributes to its freezing quickly; for so it cools sooner. Hence many people, when they want to cool hot water quickly, begin by putting it in the sun. . .” Aristotle in E. W. Webster, “Meteorologica I”, Oxford U. P., Oxford, 1923. And it was re-brought to the attention of modern science by a Tanzanian named Mpemba in the late (19)60’s.
I would try this at home, but my freezer is too full!