General Aviation is a category that covers a circumstance of flying rather than of aircraft. I think if you've got the necessary time and money to buy your own personal jetliner, insure it, get all the paperwork signed off for it and for you to fly it as a hobby, that's still GA, although where somebody with that much time on their hands gets that kind of money escapes me.

Some mere millionaires own jets with decent performance, aircraft that in capable hands could fly well in most weather but they're still GA and too many of them still die in bad weather.