The tube collecting that oil is BP's first success at containing any part of the leak, after weeks of failed attempts. The company also is readying a top kill operation for next week in the hope of plugging the gusher for good with heavy mud, though the technique never has been attempted at the 5,000-foot depth.
Suttles defended his company's actions in the face of mounting criticism and claims that it has misled the public about the size of the spill.
"We're fighting this thing as best we can," Suttles told "Good Morning America." "We've mounted the largest response we've ever done in the world. ... I understand the anger, [but] I don't know of anything, absolutely anything else that we could be doing."
BP has repeatedly stressed that every decision made since the spill has been made in collaboration with the government, but in some quarters there is a growing fear that too much is under BP's control.
BP has an army of 20,000 employees working on the response, and some people ask if the company exerts too much influence on everything, from the information out in the gulf to the response in the halls of Congress.
Labs being used to test everything from water to the wildlife are all paid by BP, to the frustration of some scientists.
"There is a perception that this lab in Texas, there is a cozy relationship between this laboratory and the oil industry, including BP," said Taylor Kirschenfeld, an environmental official in Escambia County, Florida.
BP's tentacles spread far. As the world's fourth-largest company, it shelled out $20 million on Washington lobbying in 2009, and it has some big political guns on its special advisory council, including former House majority leader Tom Daschle and former EPA administrator Christine Todd Whitman.
And less than a year ago, a former BP executive was appointed to head a division of the Minerals Management Service, the very federal body meant to police oil drilling.
"One of the big problems is that the oil industry has been so active in the process that creates regulations, that even the fines that can be levied are so limited they're just really a cost of doing business," said Danielle Brian, executive director of the Project on Government Oversight.
BP also controls the cleanup of the spill. It has taken the lead in deploying skimmers, and until today, had sole discretion in the dumping of dispersants on the oil.
The company also had effective veto power on releasing information about the spill, until Congress strong-armed it to release the live, streaming video of the site zone.