You're right, I think. I can't find information on when Aloha may have originally gone public, but Wikipedia's entry on Aloha says… "In late 1986, [Hung Wo] Ching and vice-chairman Sheridan Ing announced plans to take the company private, and it remained in the hands of the Ing and Ching families until its emergence from bankruptcy in 2006…"
The infamous "convertible 737" accident occurred in 1988 (I remember it all too well) so the return to private ownership doesn't appear to be at all connected to the accident.
So, I stand corrected. I hadn't remembered Aloha being publicly held. Blame my memory cells, they've got a few (air) miles on them. ;-) Thanks for setting me straight.