I think the real question is, are those corporations acting in a free market or are they leveraging the government for their position. I think it's fair to say most big corporations leverage the government to do what they do, and that's not anarcho capitalism, that's fascism.
Discussion
Without a state, they, as the wealthiest organization around, will simply become the state. Believing corporations will respect your rights without being forced to is even more naive than thinking the state will.
In a free market they don't have to respect shit. Normal people actually have the power to walk away from them. If they don't may money, they aren't big corporations any more. They use government controls, tax breaks, and subsidies to maintain money and control. They idea of anarcho capitalism is that I have the power to make a good life for me because no one has the power to control me.
They have the power, but not every consumer can be a fully informed one. The free market isn't that great at that sort of self regulation for just that reason, punishing businesses at the cash register for poor behavior requires knowledge of that poor behavior be spread across huge chunks of the market. Yes, there are cases where this happens, but companies get away with poor behavior purely due to public ignorance way more often than we'd be comfortable with if we knew.
And whose going to force them to respect without a state, dumbass. We would. That's anarcho capitalism.
Oh, no, I fully understand that you think that will happen. I just think it's way too optimistic. Most of the time, either not enough people will care enough to try, or the business funds enough retaliation to dissuade another attempt. Sorta like it is now with the state. Most people don't want to do that. They just want to live their lives with minimal trouble, and most will cede what they see as a few small rights they don't really need in exchange for peace and security.