That one was include on the Closure VHS set. But Trent also share vocals with David too.I’m not sure it counts as a cover, but I have a bootleg of David Bowie singing Hurt from the Outside tour.
The question about it being a cover comes from the fact that Nine Inch Nails were the opening act on that tour, and Bowie’s backing band as well. Trent Reznor was a producer and key collaborator on Outside.
The show started with a NIN set that ends with Hurt, but when the vocals come in, it’s Bowie instead of Trent.