My straw man is satire, just an echo of the OPs argument in reverse.
If I were to argue anything, I would argue that the current system failed because of corporatism or "crony capitalism". Because of government regulations, BP has a ceiling limit on what it is liable for in damages. They may pay more, but that's really an issue of public image rather than legal liability (some would argue this is what keeps BP in check in the absence of gov't regulations, but I'm not even arguing for less regulation). Government is aiding BP, in exchange for money to win future political campaigns. BP gets to try and make as much money as possible free from the regulations that hamper its competition, thanks to government.
Pro-capitalists blame the government. Anti-capitalists blame the corporations. This is a false dichotomy: both groups share blame, because the system is increasingly set up so that the two of those groups benefit. Meanwhile the third group, the people, have to suffer.
"We're talking about giant, ridiculously wealthy multinational corporations. The government is the only hope that people have of making any sort of stand against them."
This is where we get into opinion that neither of us can argue. I don't fear a corporation, because they only have as much power over me as I give them. I fear the government, because they have a monopoly on legal use of physical force. A corporation cannot come into my home, armed and without invite; the police can. A corporation cannot falsely imprison a person without consequence; the government can. BP is giant and ridiculously wealthy precisely because the government enables that behavior through back-office deals and anti-competitive laws. They create a system where I have little choice but to buy gasoline from BP, because regulation and favoritism has made it too costly for any new competition to do business against BP.
As I said, I'm not arguing that the existing rules on off-shore drilling should be eliminated. That's someone else's straw man opinion of the libertarian position. I'm arguing that, even with all the perfect regulations in place, BP can just pay some Senator and somehow get temporary exclusion from those regulations. Regardless of what other problems the "free-market" may come with (and libertarians rarely argue that those bad things don't happen, just that government tends to make them worse), at least "hands-off" capitalism means that the politicians can't give favors to these corporations and enable this kind of behavior further.