I too had alligator skin (for years and years), and I'm the total opposite of your friend; I never lay out in the sun. How I finally got rid of it - I started rubbing pure coconut oil (from the health food store) into my skin every night before bed, and when I woke up, I did the skin brushing, followed by a warm shower, followed by a cold one - that was the kicker. It revitalizes your skin and really stimulates your natural oils and brings blood to the surface, like the brushing does. Also, drink tons of water!
My skin went from alligator hide tough to baby butt smooth in about a week. Coconut oil is amazing for your skin!