Because he claimed to have it and can expect to be told to show it. Because it is rather easy to gather this type of proof from the logs produced by X' servers.

Because he claimed to have it and can expect to be told to show it. Because it is rather easy to gather this type of proof from the logs produced by X' servers. This combination - the claim to have the proof and the fact that it is easy to produce it - makes it unlikely that his claim of being able to prove his case is false.