I agree that a character is much more than what is on the sheet and it is often at this higher level that interesting details emerge (like why a character with a 7 INT is good at combat tactics). But a player, IMO, should at least consider and weigh his attributes when designing the personality. If a player hands me a character sheet with background and I see a 3 WIS, but the character is described as a worldly sage known for his keen observation and intuition, I am going to do a double take and ask him to justify it (I am not sure this one can be justified but it is an extreme case).
Glenn Beck.