I think that I would agree with such a statement; it is true that the way others treat and call you affects how you view yourself, and thus how you perform and what you achieve. You just need to look at schools to see this in action. When students in a school call a particular student fat, even when they are thin, doesn't that lead to them becoming self conscious, and either becoming depressed about their weight and sinking into a spiral of eating and gaining weight, or trying to lose so much weight even when they are thin and starving themselves.
On the other side of the coin, there are also positive benefits to the effect other's views have on our own self images. If people are supportive and encouraging of you, giving you honest compliments and praise, then generally you would feel better about yourself and happier to be you.
Speaking from my own experience, I can personally say that when others view me in a negative light (and make remarks in that regard), it discourages me from whatever I was trying to achieve. Now, it doesn't necessarily make me give up, but those remarks do give me pause and make me wonder about myself. On the other hand when I receive compliments and praise, I tend to feel good about myself and encouraged to keep on doing what I was doing without needing to pause and wonder about myself and my choices.
Thus, the statement works both ways - in other words, the views of others tend to tint the glasses that we view ourselves in.