I noticed on National Geographic channel yesterday that Germanicon uniformed soldiers were carrying No1 MkIII rifles. It was only the one episode of several that followed back to back. The soldiers, may or may not have been German. It was likely they were from some other Axis country.
They looked like they were either prison guards (POW) or maybe railroad or highway police. Hard to say. The time frame was only a minute or so. I've seen this segment, once before.
I've also heard it rumored that Axis forces, augmented their armaments and short supply of Mausers, by issuing captured equipment to rear echelon troops. It was common on the Russianicon front and I know a lot of captured Frenchicon, Polish, Czechicon and Belgian equipment was utilised as well. Why not perfectly good NoI Mk III rifles.

Jean Plamandon had several "Austrian" police marked NoI MkIII rifles for sale last year.