As a concept, the "illusion of influence" is like being "partly pregnant".
It either is, or it is not.
People pretend to have influence all the time, but most of them are not a child of the President of the United States, in which case: it's no illusion.
Of course, the President is not obliged to act in service of such influence.
But when millions of dollars can be shown to have been exchanged between the parties and demonstrable actions taken as a consequence... it's a safe bet that the influence peddling was successful, as intended.