The crust doesn't, but for the love of all that is good and scientific, stop peeling your veggies people! Carrots and potatoes especially. Almost all the nutritional value is in the skin of those two, and probably most other, other than peanuts, legumes.
Just remember to thoroughly wash the skin, and cut out any "eyes" on the potatoes or potential small scale rotting. Pesticides aren't something that your gut wants anything to do with.
I'm a chef that has studied nutrition as much as I can, for green and leafy veggies that is absolutely true, but those aren't the ones that people normally skin.
The legumes that I specifically pointed out have a ton of vitamins that concentrate in the skin specifically, and those are the "vegetables" that the layman has a tendency to skin. The center is mostly starch and sugar.
Right. Carrots and potatoes are legumes now are they? The commenter replied to you summarised it for you, and you don't know as much as you think you do.