Jason,
Rust is iron oxide, which as the name suggests, is a result of oxidation of iron, a fairly simple chemical reaction. Oxidation, also as the name suggests, takes place due to exposure to oxygen. You don't have to have water (humidity, rain) or salt (sea spray) to initiate oxidation, but those factors certainly act as a catalyst to the reaction, increasing the reaction time. In short, barbed wire close to the ocean or exposed to rainfall will rust faster because of the catalysts available.
The comments about humidity are certainly correct, but sure, iron will rust in the desert, just not as quickly as on the coast. As another post said, that barbed wire had been in north Africa for a long time and it came there by sea.
I can't speak from north African experience, but I have spent a lot of time working in arid and semi-arid areas of Australia where rainfall is minimal; wire rusts in central Australia, so I therefore assume that barbed wire did (does) rust in north Africa.
Hope this helps.