I think that during the Brain of Morbius it was not establish yet that Will. Hartnell was the 1st Doctor. But both arguments can be correct and even so a third one, that the Doctor is more ancient and had 12 previous lives (Morbius doctors has one person calls it) and with the "Loombs" idea, he manage to pass some genital material and give birth to a child that will became the Doctor!
http://meshyfish.com/~roo/index.html
The person has compiled a lot of information from the TV Series, novels, books, etc! It's a fan site but at least it has a lot of info about Who Universe!