There are really good fundamental reasons to set it off from scratch too - once you program anything into it beyond the rules you have to fix on some sort of abstractions to definite it all with. Get those wrong and you can really limit its ultimate strength.
A bit like how using existing Go games to train AlphaGo left it with some ultimately unhelpful human derived hang ups....
Deep mind are showing fairly strongly it works better to let the computer pick these sorts of things out itself
Nothing left for us to do but worshipping our silicon overlords
The other thing about the training is that I presume that those 3 billion games won't have all been purely random by any means - the first X% will have been, later on it'll have been a mixture of 'intelligent' and random moves and near the end it'll have been playing nearly all intelligent moves.