Can a temp agency hire you to work for a company you've been fired from?

Please help settle a debate my wife and I are having. It involves the question of when you work at one job, but through an employment agency, who is ultimately responsible for you and who can say if you are hired or not. I say that if you were fired from the company that you are sent to work at, they can reject you, my wife says that you are now working for a totally different company and that the client company has entrusted the employment agency to hire on their behalf; if they felt you were ok, so should the client company. What say you all?