BP was not telling the government what to do; even worse, BP wasn't even bribing the government (as far as I can tell) to ignore its transgressions. It seemed that BP was merely working within the constraints that the government had imposed (or had relaxed) and then the predictable happened -- there was a spill. That spill is obviously BP's to clean up -- they have the money and technology -- but that spill was the result, predominantly, of incentives that the government established.
Note this last observation: the government is to blame NOT for the immediate blowout, but for establishing the rules of the game that allowed it to happen. As Thomas Sowell is fond of saying, the important question in politics and policy is "and then what?" and the "then" here was the spill that WOULD result from government's failure to properly regulate drilling. (Ironically, that's the title of a recent interview with Paul Erlich, a man who made a bad bet with Julian Simon.)
Now, let's assume a different scenario -- where the government gave the drilling lease and then made BP responsible, 100 percent liable, for any spill that occurred. In that case of strict liability, BP would bear all of the responsibility and all of the blame for the spill. But that was not the case. The government was telling BP what to do (or not), and BP followed those rules (again, I am assuming that BP did not break laws).
Bottom Line: There is the game, and the rules of the game. BP lost the match (caused the spill), but only because the government's rules made it so (made loss more likely).