Final answer:
The statement is false because athletes are not primarily categorized just by the reasons they play and payment status. They are also categorized by competition level, the sport they play, and their skill level, as well as their socio-economic backgrounds and the opportunities sports may provide.
Step-by-step explanation:
The statement that athletes are categorized primarily according to the reasons they play and whether they are directly paid to compete is false. Athletes are classified based on a variety of factors, including the level at which they compete (such as amateur or professional), the sports they play, and their skill level. The drive to play may come from various motivations like love for the sport, the lure of fame and fortune, or as a path to social and economic mobility.
For many, especially from socio-economically disadvantaged backgrounds, sports are viewed as a viable path to economic security. This is evident in areas with higher production of professional athletes, such as factory towns or impoverished rural areas. The commercialization of sports has also reversed historical attendance trends, with wealthier athletes now competing in front of a 'common' audience. Thus, while remuneration is a factor, it is not the primary categorization method for athletes.