Yes, absolutely sure. There is no tether hole. There isn't even a "back" to remove, the bodyshell being moulded as one piece in a nod to style and slimness but with side effect that when the battery wears out or something fails, the phone is replaced. (In practice, there are tutorials on the web explaining how to extract the screen and gubbins from the case, but it is not intented to be taken apart by the owner, or for the faint hearted). I'm lucky that I have completely free choice and don't pay for my phones, so this potentially quite serious design flaw became a non-issue compared to what I like about the phone (of which there is plenty to like).
I already have a case - and from Amazon ("South American River" in my original post was the clue!) and which works perfectly as something to grip - but I want to do away with it because it brings other disadvantages. Thanks anyway.