Only during the induction phase. You reintroduce those foods after you lose some weight.
I never did the Atkins induction stuff, but followed Barry Groves Natural Health and Weight Loss. There are a lot of overlapping things, but no overly restrictive induction on the Groves' plan.
Another point about dairy...many people have dairy intolerances and don't even know it. They discover their condition when they try to reintroduce dairy after stopping for a few weeks. I think more people have a problem with grains and sugars, but there are those who are shocked to discovery a lot of health issues are tie to a dairy allergy of some sort.
"Somewhat less than 40% of people in the world retain the ability to digest lactose after childhood. The numbers are often given as close to 0% of Native Americans, 5% of Asians, 25% of African and Caribbean peoples, 50% of Mediterranean peoples and 90% of northern Europeans. Sweden has one of the world's highest percentages of lactase tolerant people.
Being able to digest milk is so strange that scientists say we shouldn't really call lactose intolerance a disease, because that presumes it's abnormal. Instead, they call it lactase persistence, indicating what's really weird is the ability to continue to drink milk."
http://www.usatoday.com/tech/science/2009-08-30-lactose-intolerance_N.htm