There seems to be little video footage of Anna and the black leopard physically together in the documentary. How can we thus be sure if Anna was truly communicating with him?

Everyone, including Anna, always has to be on the opposite site of the fence to Spirit as he is not a tamed leopard, and never will be. He doesn't ever want physical contact or touch from a human, and so the aim of the park has never been to try and get close to him. For anyone trying to do so, it would be fatal. In Spirit's communication through Anna he made it very plain that he wants to be left alone with no demands made of him. Fortunately, this is exactly what his caregivers have agreed to – and hence he remains a happy cat who is never bothered by humans.