Can BP plead the Fifth? UPDATE: No, they can't

Via the Times-Pic is a story from the Associated Press:

Gulf oil spill investigators say bottom of sea at explosion site is a crime scene

This story explains how (1) the failed blowout preventer and burned up rig are evidence that will probably be used against BP in court and; (2) how BP and Transocean are probably the only parties who can retrieve all the goods.

My question is, does BP and Transocean have a right to decline retrieving and surrendering evidence that it knows will be used against them?

Why wouldn't these two companies tell Holder to screw himself and go fetch the evidence with his own resources? Is there a Fifth Amendment issue here?

If I were Bob Dudley, I'd have a sit-down with AG Holder and Thad Allen, the retired Coast Guard Admiral who's been the government's point man for the response and cleanup.  I'd explain that BP is willing to do all it can to assist the government in its efforts to determine what went wrong, and help develop technology and procedures to prevent a recurrence.  But I'd also flatly explain that there's no way in bloody hell that I'm spending my company's resources to recover and surrender evidence that will be used against my company in a court of law.  Either you give BP immunity from criminal indictment, or all that stuff can sit down there on the floor of the Gulf of Mexico until it rusts away.

Gimme some feedback in the comments.

UPDATE: Gabriel Malor, an Ace of Spades HQ co-blogger and legal eagle, explains in a series of tweets (here, here and here) that the Fifth doesn't apply, and that the government probably can compel BP to surrender evidence, even if the company knows the evidence will be used against them.  That said, I'd still make the government have a court force me to do it.  To voluntarily spend millions salvaging the equipment located a mile below the surface, only to have the equipment immediately "arrested" by a US Federal Marshall and subsequently used against me by an army of government and trial lawyers, seems foolish.  It's like handing a mugger the weapon that you know he'll use to blow you away.