So I don't know about tattoos, I'd assume it has something to do with how rapidly such a thing could be reproduced and the financial impact on the owner of the original work.
But I did just run across the story about deadmau5 the DJ. He had a ferrari wrapped and rebadged, called it a purrari, and drove it. Then when he announced he was going to sell it, ferrari sent over a cease and desist.
The issue with this car was not copyright/trademark infringement, but an agreement purchasers of new Ferraris sign which gives the selling dealer first right of refusal if the purchaser wants to sell the car in the first two years of ownership. This prevents car speculation/flipping with their limited edition models. It requires that the car is in as-original condition so the dealer can buy it back and sell it again at controlled prices. The DJ removed the wrap and put the original badges back on the car and sold it back to the Ferrari dealer in the end.