Not true, obviously a written contract is the best way of recording it, but not every written contract is necessarily enforceable, and there is also such a thing as a verbal contract, or a part verbal part written contract.
It is harder to prove, but not impossible by any means; for instance in some cases conduct following an agreement can be used as evidence that there was an agreement.
If you agree to sell me a house, I pay you by selling mine and then you renege it's fairly clear that written contract or not you are in breach.