Personally I don't think it makes all that much difference in terms of effect on your physique (hand spacing I mean) but do what you think is right. It's just that I really respect the opinion of the person who gave me the advice. Plus I feel like I'm stronger whether pressing or pulling when arms are perp. to the ground. Maybe it's just me but it seems to work.
When I do pullups my grip is just a tad wider than shoulder width (same as it is for push press, military press, deadlift, cleans, etc.). It's narrower on chins (pretty much exactly shoulder width or just a bit narrower) b/c it has to be to keep forearms perp to ground.