Halliburton had just done a cement job on the well- 20 hours earlier by their own statement. (See the link I left in post 51).
To confirm what others have stated:-
1. Drilling rigs are rarely owned by energy companies. They are owned by drilling companies, one of which, Transocean, had the Horizon Explorer built.
2. The rig was indeed under contract to BP. (There may be other companies involved, or BP /Amoco may be the sole shareholder.
3. Specialist services on rigs are performed by service companies, who are either contracted to the Operator (BP in this case), or subcontracted by the Drilling Contractor. (Transocean).
4. Trransocean is one of the largest Drilling Contractors in existence. It is a U.S. company , registered on the New York Stock Exchange.
5. The rig and virtually all personnel on board would be American. It's hard for non-US citizens to work in the US domestic sector, though many American expats work abroad. The person in charge of safety and environmental concerns on board would be the Transocean Offshore Installation Manager, (OIM). BP personnel probably numbered as few as two and almost certainly no more than a handful. (Even those may be consultants). They are there to make sure the contractor follows the well plan, meets all appropriate regulations and standards and does not waste time.
6. In a case like this, a well plan would be submitted to all the appropriate US Federal and State authorities, long before permission to drill would be granted. Rigs are subject to all the same inspections as any merchant vessel, plus a lot more. The design specs of the rig and particularly the BOP would have to be approved by the authorities. The well plan would then be followed pretty much to the letter unless some unexpected fact required a revision- if , for example, the reservoir turned out to have unexpectedly high or low pressure, when a change to the density of the drilling fluid might be proposed on engineering grounds. This might have to be approved by local regulatory bodies. (I don't know the US situation, but I expect it would be at least as strict as Kazakhstan- which, by the way, has had extensive environmental regulations since long before 2007, despite the quote in post 61).
7. If BP and Transocean followed the approved plan and did not do something unapproved or stupid, it's hard to see in what sense they are responsible for the catastrophe. They did what they had permission from the U.S. Government to do.
This is , of course, the question of interest:- what exactly went wrong here? I remain baffled by the varied versions I've heard. I'm apt to accept the Halliburton statement (because that's who I work for and I can see no reason for a lie, especially one so easily checked- that they cemented the well 20 hours earlier.
This may have been a multi-stage cement job. It appears something went very wrong afterward. Most simple scenario is that on pulling the cementing string (of drillpipe) out of the well after the cement job, they did not adequately fill the well with drilling fluid. This might cause an influx of oil or gas to enter the well.
Another possibility is that the Blow out preventer (BOP) stack somehow unlatched at the sea bed. That would mean the hydrostatic head above the sea bed would drop from whatever the existing mud density was, to the density of seawater. That difference might be enough, again, to allow formation fluid into the well.
But. If standard procedures were followed, neither scenario should be remotely likely. Also, if the well had been cemented in, there should have been no possibility of formation fluid entering the well.
The telemetry data from the rig should be on record in BP and Transocean's onshore offices. Both companies must have a very shrewd idea of what went wrong.
This information ought to be disseminated immediately, but is probably being restricted due to the ongoing legal cases.
If this scenario continues to worsen, it may be as much a failure of the legal system as of any engineering system.
Incidentally, here's a link to the rig stats , from Transocean's own site. Damn nice rig.
http://www.deepwater.com/fw/main/Deepwater-Horizon-56C17.html?LayoutID=17
Incidentally- the rental rate was about $520,000.00
per day. This sort of operation
costs. 
