What is your main issue here? Chicago or the Saints?

To answer your question, it is not either/or it is a little of both.

Raw talent has to be coached, ball hawking is a mix of natural physical ability and vision. It doesn't help if the player hasn't been coached as to where he needs to be to use his skill set.

A second set of eyes on the sidelines is invaluable.

For example: Tiger Woods has natural ability, his coach teaches him how to use it.

as for the title "overcome coaching"... I am not sure what you mean.