I have a brother-in-law in the military, and he often gives times that way. I always have to subtract 12 to figure out what time he's talking about! You're right: it is funny.
*LOL* I get that's funny for not Europeans. *grin*For me it's totally normal and useful. One don't have to say a.m. or p.m. (always) to make clear which 4 is meant when something has happened or you tell someone something. If you use 1-12 until noon and then 13-24 until midnight you always know in which time something has happen and you just has to say/write one count. It makes everything clear.
Kirsten has a very good point: it could be really useful, and cause fewer mix-ups than our 12-hour format.