I have seen a lot of items for babies online and at shows, made out of linen. Not sure it is the same type that your friend bought, but it is the "new" thing. It is more like gauze than the thick linen.
Benartex
http://www.benartex.com/catalogsearch/result/?q=linen
makes quite a few lines, as well as a couple of others that I can't remember. I don't know how it launders (it is like gauze), but it is soft.