How private is private aviation?
Not very.

The jets have transponders and people have scanners and pick up airport signals. Everything is registered and universally identified in the air.
The extent to which current or former police officers and others with the law enforcement or political connections to obtain private pilots’ licenses are able to keep the details of their flight and air traffic operations out of view of the general public is debatable.
There are people with no secrets to keep at the golf course who are suddenly surprised when outsiders to their club or those under a certain income level learn of their activities.

Major white collar criminal groups already have this information, whether or not they choose to post if for the popular press. Otherwise, if jets were not easily trackable, there would be a huge theft problem.