In The Story of Stuff, the narrator claims that because corporations are larger than many nations in terms of sales and GDP, they are able to use that power to steal from the third world and trick us into consuming more than "our fair share."
Corporations may have huge amounts of money passing through their hands, but they cannot coin money or use force to get what they want. Their power is limited; if they begin selling products people don't want, the company loses "power" and income, and eventually fades from existence. When government does the same thing they do not lose any power, and no one has permission to offer a better product (or to buy a better product) in many circumstances, like first class mail, road building, driver licensing, etc.
This argument in The Story of Stuff is similar to claiming that because a doctor makes $800,000 per year he has twice the power and influence of the president of the United States, who makes $400,000 per year. The president is tremendously more influential/powerful, just like governments are more powerful than corporations. Additionally, small groups of organized people have more power to influence the government's actions. This is counter-intuitive but makes sense upon closer examination. A small group with a cause that makes polititians look good is a more attractive way for them to spend tax dollars.
For example, $150 million will make a huge difference in the lives of a small group of corn farmers (and will only cost citizens of the USA 50 cents each) but would be meaningless for Exxon mobile; their total revenue exceeded $475 billion last year. Further, large corporations are owned by millions of people. Increasing corporate taxes simply takes money from the owners, who are primarily (either directly or via mutual funds) regular people who have purchased stock in Starbux and Wal-Mart.
If you take a closer look at the references for The Story of Stuff, you'll find some gross errors, including the claims that 50% of government spending is for military, and that we have lost 80% of our original forests. The primary message is that we are destroying the earth and the third world when we buy cheap products, and that the products are cheap because the externalities of production (pollution and destruction of the workers and environment) are not included in the price. The realities of the situation are more complex, but we are inclined to believe it is as simple as the film implies because of our natural tendency to think of wealth as a zero sum game (where one man wins only at the expense of another) and abhor waste. The film prays on our ignorance of basic economics and general failure to understand the source of wealth on earth.