being unique vs. being one of the mass

When I was in the US I've noticed that being unique is a key to success. Everyone is trying to be different in any possible way. Even professors encourage their students to explore their personality and bring something unique to their projects and homework. Providing an example from personal life is totally fine for a class discussion, while back home only example where situation is true not only for one person but for many counts as a good example. Cultivating uniqueness is still not at its peak here. Everyone is still a part of mass although some are slightly different.
I was reading an article today which was telling about a girl. It said something like this: this girl is so talented: she 's a wonderful artist, she writes poems, she's one of the best in her class at school - well, basically like many other kids around. First part of a sentence is fine, but second part is some kind of equalizer. I guess it is still not completely acceptable to admit uniqueness. Even when people talk about their successes in life they would add at the very end, that it's just normal, just like what other people have or achieve. There's a strong tendency to refer to oneself as one of the mass. This is a great cultural difference.
Americans say 'I', Russians say 'we' and 'people.'