I know nothing of what the military specifies for their aircraft or these types of equipment, I'll assume it's of a higher grade than I need in my corporate LAN.
Regardless, fiber is tough enough to run through conduit, can be bent around corners (not right-angle turns, perhaps) and for my use, can be spliced together in the field with a piece of plastic worth about a dollar and some inexpensive tools. The military can afford to wrap the fiber in something protective to prevent kinks or breaks if they wanted, and maybe even design connectors and transceivers that will stand up to more shock or abuse than your typical switch/router patch cables and transceivers. Point being, it's a robust technology that's been in use for a fairly long time (relative to computer tech).
From TFA, it sounds like they're multiplexing a lot of logical connections into a few single physical connections. How many different systems are required for an F22 to fly at combat readiness? How many of those systems have interconnected parts requiring their own communications? Running entire systems' electronic conversations over (relatively) few fiber cables sounds incredibly more scalable, and if the initiative works, reliable than point-to-point or -multipoint copper for each device. I suppose "a lot" is an understatement.
How'd you like to see the book of checklists for a system that has miles of potentially faulty copper? You can troubleshoot that one, I'll do the one with a bundle of fiber I can count the number of strands on. :)