The definition of "arrangement" is, as you point out, general in the sense that it would not require.... I'll preface it by saying that the interpretation of all this would be up to a commissioner and eventually to a judge of the Federal Court if a decision were to be challenged.
An arrangement wouldn't need to be a written contract. It wouldn't necessarily need to be spelled out on paper. It can be a verbal understanding. Ultimately, it would be up to the commissioner, based on the facts available to them, to determine whether there was an understanding, an arrangement, an agreement to conduct these influence activities. It's purposely drafted in a way to not limit it to just that one contract that says I will pay you X to do Y.