I feel that the rules should contain some examples. I spent a while battling a puzzle to realise that I had been interpretting "No more than two similar numbers next to or below each other are allowed." as "A box must have no more than 2 neighbours of each number" i.e. Exactly 2 0s and exactly 2 1s in the non-diagonal neighbours.
I think that what's being referred to is runs of numbers, so if you see 0,0,_ you know the last one must be a 1