Just because the idea is kind of neat: It's possible you're getting jumped on by the lawyers here because "legal proof" itself is such a non-legal concept. There's such a thing as mathematical proof, for sure. There might be such a thing as scientific proof. But you could rarely point at something and say "that's legal proof." You could only say, "that turned out to be enough evidence to convince that particular jury." "Proof" is defined by the observer (jury, judge, etc.), not the object (contract, bloody knife, etc.).
He did have a contract. It just wasn't written and signed. It's still a contract. The CFO is misleadingly implying that because it was not signed, there was no contract.