Anecdotal based on the experience of one, but maybe some other “old timers” can back me up. I was pretty confident that I deserved my place at a highly selective college when I attended. At the same time, I did not question whether anyone else deserved to be there. No one I recalled bragged about their HS achievements or test scores to establish their place in the pecking order. I am sure there were some who had less confidence in themselves and definitely people who were cocky vs people who were humble, but that just seemed to be part of a normal distribution of people with different personalities.
With D (highly selective LAC) and S (an HYPS), they seemed to be more aware of the accomplishments of others. Given the increasingly competitive nature of getting into these schools, I think kids are more tempted to brag about themselves to establish their bona fides and place in the pecking order. This then adds fuel to the phenomena that @TiggerDad points to above, which is a shame. It is unhealthy to feel as if your position is undeserved, it is healthy to realize that there is always someone smarter/better than you in just about everything, but that also means there is room for improvement for you.