I remember reading about a study about how teachers treated their students.

Teachers received a note that one of their students had been performing very badly in the recent exams. Researchers saw how that teacher then treated that student. They gave less attention to them and they almost ignored him/her. The student performed even worse than before.

Sometime after, researchers said to the teachers that they've messed up with the exams and that actually that kid had been remarkable at the latest exams. The teachers radically changed their attitude and behavior towards these children. Consequently, the students improved at a surprising rate.

We behave towards people the way we think about them, and in some way, it becomes a fulfilled prophecy "see, I knew he was bad". So we should pay more attention to how we see and judge people and understand that as you point out, see more in people than we initially realized.

Give them a chance, show them our appreciation, and they'll surprise us ;)