As I remember, when Trump's token was first launched, several news reports emerged claiming that insiders were buying up the meme token for millions of dollars even before Trump's official announcement. So, personally, I also think that not only is his son involved in this dirty game, but also most of his entourage.
His personality has reached the level where he is, as the president of the most powerful country in the world, any of his activities will be highlighted by all the media more than the activities of any other general. I think that's exactly what happened here.
But from his position he did not play a responsible role because they tried to do one kind of rugpull through the trump coin launching. But what you said could be true because it could be that trump hired the media just to promote his point?