The EPA Directed BP to stop using Corexit 9500 and come up with a substitute in 3 days. BP objects.
Who is right?
Unless one has full data and knowledge of the properties of the dispersants, it is impossible to advance a valid opinion.

I would tend to side with the government agency, EPA, but I can't support that opinion with data or facts.

The article linked by Ed T. says BP's use of the dispersant is "unprecedented" at the depth, and volume of the blowout. In other words, the method is untested and may be pissing against the wind.
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Only one of Costner's machines can handle 200 gallons of water a minute. The others are smaller. Manufacture of 20/month doesn't help much. Would BP authorise the cost?

BP is not trying Costner's idea, they are permitting Costner to operate one from a barge. In this way they cannot be blamed for failure of the method.
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We can hope that the mud-junk-cement capping to be tried next week works or cuts down the flow to a much lower level. If that doesn't work, the offset well(s) will take at least 2 months to do the job.