Shouldn't purchasing the tattoo transfer the rights to the person being tattooed?
AFAIK, this still needs to be explicitly stated in the agreement/contract. by default the creator always owns the IP they create (in the US). this is why software companies have to explicitly state that they will own the product of your work when they hire you.
Though it is kind of funny when it goes for a tattoo, just never thought about it. It is not like you want to have contract for a tattoo unless you are LeBron...