C&D notices are, in theory, courtesies and don't usually include evidence. If you aren't doing what the C&D says that the person issuing thinks you might be doing, then you have nothing to cease or desist.

The goal isn't to convince you of the facts of your action (it may be, in part, to convince you of the impact of the relevant law), so there is no purpose to include evidence.

If they decide to file a lawsuit, then evidence will become an issue.