Did BP have the right...

Better to show BP because of the large amount of people that work for them and there families will come see the movie and buy tickets.

I'm sure they did, they had to make the money back somehow

I wonder, since it based on true events, whether or not they could have stopped it.

its free advertising for them

It's a form of "full disclosure" and damage control. Here's a movie showing what happened. Bad decisions and assholes involved. But they're not boogeymen anymore. This is something we can all wrap our head around and move on.