I think there's more to it than that -- there could be a cultural aspect. Some black fraternities brand their pledges once they're accepted into a house -- I knew several guys who had the Greek letter Omega branded on their arms or chests.that's fraternities in general. has nothing to do with race.
Whether it's a "slave thing," or something else, I think the branding has some special symbolism.
I've only ever heard of branding being done by black fraternities.