They may not be true in every case. So problem solving is one of the places where cooperation is especially good. Let's also talk about some of the possible drawbacks of cooperative learning or some of the arguments people might make against it. We knew you'd bring that up. It's a myth.
Motivation is based on the subjective possibility of success.
If students feel they have no chance to succeed, there's no motivation. In a typical class, maybe 10 percent of the students think they can get the highest grade. The other 90 percent know that they don't have a chance in the world. Therefore you tend to get motivation out of a very small section of a class. Also, in competition you only work hard enough to win.