Haven't got the Oregon mount with me right now, but from memory the curvy bit is double-curved, so that you can mount it on either stem or bars without rotating that part.
I remember concluding I would need a new set of zipties if I wanted to swap it between bikes.
The mount is same for Oregon and Dakota, and ^ that is how it works. The cable-tie holes are quite small and re-usable ties tend to be wider. I just buy cable ties in bags of 100 for about £3 from the local hardware store, and always have a bundle of spares in my cycle luggage.
As I see it, the problem with stem-mounting these models is that it is very useful to be able to adjust the angle while riding, to get the best out of the rather difficult screen visibility. This can only be done if you bar-mount, not stem-mount. I found that the Dakota screen benefited greatly from being angled somewhat towards me (so that the surface layer is reflecting my body back at me, and not the sky).