Aviator, I think what people are referring to are the lessons that can be learned in the 'school of hard knocks' - especially as those lessons relate to command decisions. The lessons of living with the consequences of a command decision that you have made under difficult circumstances with often no one else to defer to. The lessons that grow that sense of 'rat cunning' and judgement over a variety of backdrops of aircraft types, physical environments, companies, personalities, the list goes on.
Sure, experienced captains can pass on excellent flying lessons and experiences to the one sitting next to them. BUT, it is not the same as experiencing them for yourself and while alone in the hot seat.
Airlines are excellent at requiring sound operating technique based on standard operating procedures but ocassionally an 'out of the box' scenario will present itself and one who has had a diverse background of experiences is likely to have more to draw on to come up with a suitable response in that situation.