Wrong. The theory is that the music makes the place a more convenient place for customers. This is a public performance in oder to increase one's profit. You need a license to use the songwriter's intellectual property for this.
Er, no actually.
There have been a number of cases of the PRS fining, or threatening, businesses that are playing music in areas with no customers, including Lancashire and Cleveland Police Forces.
Indeed, the PRS themselves (links to PDF) say that it improves morale (scroll down a bit).
I've already noted that if it's in a public area then businesses have to pay; I'm referring to areas where no customer has access to.