I tend to see that comment as the end of one process and the beginning of another. While Alistair was never taught to lead, he's been able to watch good leaders in action. Eamon may not have treated him the way he deserved to be treated (Hello? Basic human decency?), but no one's ever said that Eamon wasn't a good arl. Plus, he's had the benefit of watching Duncan and then your Warden. So, I see that advice to "look out for yourself more" as the beginning of his being able to put what he's seen into practice while there's still someone else doing the actual leading. He has the basic qualities -- he's decent, honest and has a firm moral compass. Everything else can be learned. I don't imagine that Elizabeth I really thought she'd be queen either, but she certainly rose to the occasion.