If we use a split stick to record how much money you owe me, and I simply add more marks to mine, to pretend you owe me more, it's obvious that I'm cheating. But if I simply split a brand-new stick and add marks on it, then our sticks won't match up at all. How will a court know which is the original?
Presumably they had some way to sign them? After all, that's why both parties sign both contracts today. If you go change yours, I still have your signature on mine.