For what it's worth, the two important words from a Pokemon rules sense are "up to". As has been indicated in the thread "up to" does not include 0. This has been set in a number of rulings precedence. The other key words are "if you do". This links the effects of the second sentence with the first. If you don't discard any cards then you can achieve the effect of drawing until you have six cards in your hand.
I think I understand where the confusion that "up to" might include 0. It comes from deck searches (and other events) where one can fail the search, because your opponent has no recourse to check whether you failed on purpose (another tennant supported by rulings precedents in the game).