I have been told the same thing Noble Ox - a trainee chef gets told to cook a medium chicken curry over and over again until it clicks. When I am trying a place for the first time, I sometimes order that because it's such a standard. I have also been told by more than one chef that they had to train for 2 years before being allowed to cook unsupervised. Not quite the 10,000 hours they say you need to master a musical instrument, but in the same order of magnitude.
I believe it has something to do with more and more of the task becoming instinctive and unconscious, which brings me back to the point I was trying - possibly not well - to make, which is that more experienced chefs find highly condensed recipes more intuitive and useful than the slavish lists of ingredients and processes that we find in most cookbooks. So there comes a point at which the request "Could you write down the recipe for me?" becomes hard to fulfill. Maybe a more useful question would be "Can I film you doing this?" which has always worked better for me,