BP can't rely on the Limitation of Liability Act of 1851 act. First of all, they caused the accident (I think this is what "privity" means in this context). But more important, the 1990 Oil Pollution act supercedes the 1851 act in this situation.

Finally, the value of an offshore oil drilling platform that has burned and sunk in several thousand feet of water is not $27M, it's zero.