You are absolutely correct. An unloaded Springfield or Mauser is just as safe as a Blaser with a round in the chamber.
It may come as a surprise to some here, but I suspect others have had the same experiences I have, but I have never left a vehicle, camp, or a boat in Africa this without a round in the chamber and the rifle either on safe or not cocked (R8 and S2). All of my guides and PH's have been aware, and all were fine that I did so. Over the years, I can think of at least half a dozen opportunities that would have been missed either due to time or noise had I not had a rifle ready to quickly fire.
Had a PH asked me to march around with an unchambered round in non-dangerous game country, I would have complied. Had he asked me to do so in dangerous game country, we would not have hunted.
Except for a boat in the Caprivi (at the PH's request and another story), the chambered round has always been returned to the magazine upon reaching the vehicle or approaching camp.
I am not sure why this would seem an odd way to handle a hunting firearm to anyone. After all, it is the same procedure all of us employ hunting quail, pheasant, or grouse with a guide or friends here in the States.