First of, in Europe we use ISO 8601, which is quite different from the military time which the USA uses.
Second, in my home country we still say "16 on the clock" or "15:45 on the clock" (just translated to the native language, eg. "Klokken 16") to signify we're talking time and not weight or distance.
TV time and military time don't even use 24 hours. You can have a TV show that goes from 23:30 to 25:15 (25>24, in 24h it would be 01:15).
I imagine those who call 24h "military time" also say "I'll be home from work on Friday at 4100 AM", which makes about the same amount of sense.