I have been wracking my brain for years, trying to figure out wizarding genetics. It never made sense to me how one could have both muggleborn wizards and squibs. I always figured that the gene for magic was a recessive trait, which meant that it should be impossible for two wizards to ever have a squib child.
Tonight, I found out how it works. Magic is genetically inherited in two (and possibly more) ways.
I was reading about a genetic condition called Waardenburg syndrome, which causes deafness and hypopigmentation of the skin, among other things.
Waardenburg's occurs in several types, Some types of it are autosomal-recessive, which means that a child must have two copies of the gene to be affected, and children of either sex can be affected. Other types of it are autosomal-dominant, which means that a child of either sex will get Waardenburg's even if he has only one copy of the gene for it from his parents.
I haven't totally worked out the genetics, but for me, this somewhat explains the squibs and muggleborns puzzle. I don't know if Rowling knew about the genetics of Waardenburg's, but this is just amazing and wonderful to me.
If I'm right, and the gene for magic is recessive in muggleborns and dominant in squibs (who don't inherit the gene at all), then the DE are wrong. Muggleborn wizards have to be, in fact, pureblooded in a manner of speaking, since the only way they can acquire magic is if they have two copies of the gene.