This is true! I would definitely go with the dawn. They use this to wash oil off of baby ducks and other wildlife. I have adult cats and I still use Dawn to wash them. Use the blue kind that is original scent instead of anything that has additives.
I wouldn't risk it, to be honest.
At four weeks, they're still too young to have fully developed immune systems and, like human babies, their skin is incredibly sensitive. Are these bottle babies? If not, mom cat usually does a good job of keeping them clean, but if she can't for any reason, warm water and a drop of Dawn liquid soap will usually work, and is much gentler on them, or most people have good luck with just a warm, wet washcloth.
Another point of this 6 weeks and up, its not recommended to bathe small kittens at all, unless you really must. Iths the risk of chilling them out.
I just recently bought a shampoo for my 4 week old kittens but I didn't notice that it said "For ages 6 weeks and up". Should I follow it or is it okay to use the shampoo on them now?