Sorry Gruntle, but I cannot agree. I don't think it is arrogant at all, just a polite letter, telling you, a successful applicant who has turned down their offer, that there is no point in you applying again. I would guess that a number of people in a similar position to yourself have actually gone back and said they would now like to accept.
Better, I would have thought, to know exactly where you stand instead of not getting any response at all?