Pressure of any sort is illegal under the 5th IMHO (IANAL)-- administrative remedy paperwork completed or not.
I would imagine that BP shareholders have a stake and as soon as the stock goes down, or upcoming dividends are threatened, BP shareholders have standing due to monetary damages inflicted by the president's public and blatantly unconstitutional pressure.
So far the government has not done anything that isn't allowed under the terms of the lease ~ else BP would have gone to court for injunctive relief.
The Fifth Amendment simply does not apply in this case EXCEPT for the people who are harmed, and their recourse is against the government!