Corruption is not how free markets sneak in, that's how they die.
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.