There are various non-classical logics, like dialethic systems, could allow for his statement to be correct by, for example, allowing both A and ~A. You could probably also find some way to prove using a system that limits the transitive property that the "Elon Musk" referred to in the documents is not the person speaking (or in any case cannot be proved to be the same, and therefore his statement cannot be proven false)
There are various non-classical logics, like dialethic systems, could allow for his statement to be correct by, for example, allowing both A and ~A. You could probably also find some way to prove using a system that limits the transitive property that the "Elon Musk" referred to in the documents is not the person speaking (or in any case cannot be proved to be the same, and therefore his statement cannot be proven false)