Both parties in a contract can have an incentive to lie.
I don’t think all contracts have an obvious both losing state though.
Think about two situations:
Firstly, if I lend you money, we split sticks, then I throw away my stick and get a new stick that says I lent you more money.
Secondly, if you lend me money, we split sticks, then I throw away my stick and get a new stick that says you lent me less money.
In both cases you're claiming my stick is clearly counterfeit because it doesn't match yours and I'm (falsely, but nobody knows that except the other party) claiming your stick is clearly counterfeit because it doesn't match mine.
What happens next? We're no better off than if we only had a verbal record and were disagreeing. So what is the point in the sticks?
Understand?