Not quite. Professionally flown business jets operated Part 91 have a comparable safety record to airlines.

Big distinction between the average "private plane" and a corporate jet operated by a top tier company's in-house aviation department.

In fact, many corporations with sensible risk management policies require their key executives to fly on company aircraft.

And, yes, the ones that truly get it also prohibit the same key execs that can't be on board the same plane at the same time from being in the same automobile/other form of transport.