Fantastic, I love word games. If one “acknowledges” an “allegation” of payments it is no longer permissible to refer to them as “alleged” payments. (And you are permitted to infer that some form of “documentation” exists).
(And you are permitted to infer that some form of documentation exists).
Most certainly an acknowledgement of an allegation can exist without any documentation of said allegation, so no, you cannot infer that documentation exists based solely on its acknowledgement, unless you are, in this case, considering the reporting of that acknowledgement by the media as the documentation, but I do not believe that is what you were trying to say.