The first Saab, the 92001, was indeed inspired by airplane design, since the company was started in 1937 specifically to manufacture fighter planes for the Swedish air force to preserve Sweden's neutrality.
Now, they are two different companies, and although none of them are hugely successful, the fighter jets have, as you mention, sold to several countries for a number of good reasons. I had the pleasure of working closely with representatives of the Swedish Air Force while taking these photos, and they have a very professional attitude to this project.
Here's the 92001 (not my photo):
Here here are two of the latest model, the two seat family version
D80 with 80-200 AF-S @ 80mm and f/2.8