Its not true at all, skin is a live organ, more you tear down the dead skin cells thicker it gets. I had the same misconception for a long time , I was even scared to use my microdermabrasion cream regularly, but after I read on "Dr. Denese's Secrets for Ageless Skin: Younger Skin in 8 Weeks" where she answered some of these FAQ's my understanding was changed. One of the few reason a glycolic acid peel reduces wrinkle is because over time they make your skin thicker and wrinkles dont form that easy.
I have been using 40% lactic acid peel for last 8-10 months and recently started 30% glycolic acid peel ( once a week), if what you read is true than I wouldn't have any skin left. By the way I had exceptionally thin skin; I think its way more thick now. But as you probably know that using these AHA/BHA does make your skin sensitive to sun.