OK, OK, I know no one in his right mind would use Windows on a critical system like the shuttle. (A crash might make "blue screen of death" take on a whole new meaning.) But DOS isn't the only other option. And I'm not even talking about Linux or *BSD.
There are a bunch of real-time OSes that are used in critical systems. There's Quadros
RTXC, Green Hills
Integrity,
QNX, Wind River
VxWorks, and others.
The space program is kind of a synonym or metaphor for the cutting edge of technology. So I'm surprised to have a DOS computer on a shuttle in any context. If it's not exactly the MS-DOS of the 80's, it's probably not all that different. It sounded like it was using a FAT file system.