Yep, urban legend, but as a side topic,
Contracts signed while under the influence are invalid.
Well, maybe. You have to be really, really, drunk. And the contract would probably still stick anyway. Getting out of a signed contract due to inebriation has happened before, but it is exceedingly rare.
If the story were real, the booze would be irrelevant anyway, because a contract that tricks someone into a tattoo that no one would want would be voidable because it violates the implied covenant of good faith and fair dealing by which every contract is supposed to operate.