To use your phrasing, a capitalistic view of this is that corruption is just anything that breaks the fairy tale idea that the people who work in the corporation seek the interests of the company and not their very own private interests.
You can even see it play out here on Hacker News - people who optimize for their own career goals at the detriment of the company that pays them to get a job done.
What about when a President appoints his daughter and son-in-law?
(feels like sarcasm just experienced an integer overflow, or perhaps not)
Bribery at any level is not acceptable, and even at the corporate level if shareholders are affected, they would want to remove the person taking bribes
I feel a company is responsible to its customers and shareholders, that's about it.
Free markets don't exist in a vacuum. They rely on governments to maintain a state of fair competition. Corruption does not lead to free markets, it leads to monopolies and oligopolies.
It is true, however, that unchecked free markets often lead to this state.
Free markets rely on fair competition: you want companies to compete on quality and price and remove all the other factors, like nepotism, entryism or corruption. There is a competition in corruption, but a competition that is not in the public interest.
The company getting the big plane contract in country X should be the company with the best/cheapest planes, not the one able to send the hottest hookers to the crucial decision makers.