I spoke too broadly. Leather for fixed blade knives is by definition rejected for parachute jump-certification, and is thus in effect banned for airborne troop during jumps (this apparently after many, many injuries, after which they finally settled on an outright ban for leather and fixed knives combined ).
Your claim there is no ban of any kind is likely based on the fact that they simply don't certify leather sheaths for WEARING during jumps, but paratroopers can still have them in their rucksack... Just not on their bodies while jumping.
However... Airborne troops are still part of the Army, so what I said was not entirely false either. I just misremembered it too broadly. The information was from someone in the service and makes sense. How recent that is and where the rule is written I don't know, but that leather, as a material for fixed blade knife sheaths, is banned from being worn during jumps, sounds pretty reasonable to me.
Gaston