And that's true. Except when it's different.
It is absolutely true that offering a cash reward works when the work is rote, systematic, and simple. However, it ceases to be true when the desired work is spontaneous, free-thinking, or creative. If you tell an artist that you'll pay them based on the number of works turned out, you'll often see a lot of work! But it often won't be very good work.
Teachers given salary bonuses to keep student enrolled do keep students enrolled. But grades drop. Don't believe this? Here's a study on it.
Studies on this kind of thing are starting to become common, and they seem to point at the idea that the mental effect of seeking a reward doesn't work well with creativity. Creative behaviour requires a somewhat unfocused approach; money rewards narrow your focus.
The strange thing is that money rewards given to charity don't seem to do the same thing. If I'll donate a dollar to a children's hospital as a reward for you, something different seems to happen; the mental focus doesn't narrow down in the same way. If I give a reward (say, bonus equipment) to the group you work with, it's somewhat different again. It also looks to my reading as if status-based rewards, such as trophies, can go either way depending on how they are framed.
A chain of stores offering a cash bonus to employees for 'great ideas' will often receive suggestions, but quash creative thought - they may be offering the wrong kind of reward to get great ideas. In this case, if there's some satisfaction to be gained from offering those ideas and seeing them implemented, they likely don't want to offer a reward at all. The reward is intrinsic; it's built in to the activity. Giving money to people for solving puzzles doesn't help; solving a puzzle is the the reward for solving it. In fact, giving an money reward for solving puzzles slows progress on those puzzles. This is commonly called the overjustification effect.
Socially, this means that when you're offered the wrong kind of reward (at work, at school, in a game), and you know the intention, you may actually need to fight the effects of the reward to accord with the intention. It sounds outrageous to suggest calling up your boss and saying "Hey, uh, instead of offering bonus money, could you offer us something else?", but it may actually be in your interests to do so. If you're in a position to offer rewards to others, you want to think very closely about the kind of reward you want to put out there.