Well, you do, obviously!
It's like a lot of things, if you look on and say nothing then it is as if this is okay with you. Well, for a lot of good reasons, playing dress-up when real-world skills are involved is not okay with many of us. You can read of people who pretend to be doctors and paramedics, even and this sort of pretense on JT's part can be pure catnip to the weak-minded that way inclined, to pretend to be more accomplished as a pilot than you really are is an invitation to serious trouble. Never mind that the facts are on file about his qualifications; he is posing as the Captain of that aircraft and that is enough for me.
It doesn't even need to be pure pretense to be dangerous; have a look at the Air Florida crash for an example of this.
I have no real problem with rich guys owning beautiful toys, not being a Communist. It is the pretense that bothers me, that is all. To me this is not promoting aviation per se but promoting oneself and in a rather childish way. Can you think of anyone else who dresses up in this way to fly an airliner with a PPL? This is on the level of the amateur yachtsman in his little white cap with "scrambled eggs" on its brim, as if he were some sort of admiral in real life. It's just "walting" when you get down to brass tacks.
If JT would simply get the proper licence and rating then there would really be nothing much to carp about so that it's a mystery to me why he hasn't bothered to do that. If he has the money for the airplane and the flash uniform then I am sure he has the money for the training to pass the written and practical tests so what is stopping him, given that it really will not eat up a whole lot of time? Am I the only one who has to ask this obvious question?
Any professional pilot who has no problem with someone impersonating a professional pilot, well... why then complain about those of us who do have a problem with that? If you are that amazingly tolerant then extend that tolerance to all, and best of luck with the state of things that will bring.