It was nine years ago when I researched and then bought my Rohloff. It is my recollection that there is a part or perhaps parts that will physically swell if a contaminant gets into the hub, that part(s) absorb that contaminant. And the contaminant is common in some oils. Thus, the reason to not use some other oils that you may have. I could be wrong, memories fade and change over time thus my recollection on swelling parts could be some other product instead.
In other words, if there is some part or parts unique to Rohloff that are not used by Shimano, it is unlikely that Rohloff oil would have any great advantage over other oils in a Shimano
Some oils will coat surfaces, dry and harden like a varnish. I am confident that Rohloff does not do so. I would not use any oil that I suspect has that characteristic. I have a small can of oil for lubricating sewing machines, that can is half a century old and has a heavy coat of a varnish like substance on it. Over the decades I have occasionally seen a brown coating on some Sturmey Archer 3 speed hubs, I suspect from the oils that were added by the users. I have also seen that varnish coating on vintage Campy hubs, presumably from the Campy grease. I have a small jar of half century old Campy grease, it used to be an off white but now is a light brown color. I have not seen any hardened residue from Phil grease or Pedros bike grease.
I used to use synthetic gear lube in my Jeep and Land Rover differentials and transfer cases. But I am not using any in my Rohloff. For one thing it is quite viscous and would likely add some drag.
I also have some non-synthetic gear lube on the shelf that I used for my vintage Triumph motorcycles. The motorcycles have been sold, but the gear lube is still on the shelf looking for a new home.
