Typical Trump. He always speaks under the operating premise that all significant events will of course revolve around his existence.
I don't think he even believes in that; rather, he has come to expect that people need him to pose as a mover and shaker, mostly because he has consistently drove away any who do not conform. Whether there are any facts or evidence to support his claims is a task for others beneath his notice to undertake. Or something.
In his mind, It Is All About Him (of course).
As others have noted elsewhere, the most likely scenario is that he is simply playing his character, which is that of The Apprentice's host. That was the absolute apex of his life and he never truly left that posture - or even tried to.
His supporters won't care that he is lying. He is Trump. He lies all the time. His supporters could not care less.
Trump's standard Transactional Analysis game is, as expected, a very simple and foolish one, almost elegant in its utter and proud lack of self-awareness or nuance.
- He announces something that implies that he, Trump, is a Big Deal. Bonus points if it is utterly ludicrous or makes him appear to be the target of some form of malicious action.
- If it happens, it is because of how impressive he is.
- If it does not happen, it is also because of how impressive he is.
- Any facts that challenge that tale are to be disregarded without comment.
- Rinse, repeat. "Ad Nauseam".
It is just Trump being Trump. Being the barely socially educated child that he never ceased being, with no regard whatsoever for any prices that anyone else might pay for humoring him.