Living in a world where most devices are designed for righties, lefties necessarily learn to do some things right-handed. They generally can do more with their right hands than righties can with their left hands, and generally have a better-developed comprehension of mirror image. However, they vary in the degree to which they feel their left-handedness.
For some, playing a right-handed instrument is no big deal. For others, it's a huge deal. I am left-handed with a strong sense of it. When I held a right-handed guitar in normal right-handed position, it felt so awkward that I immediately abandoned the idea of playing that way. So with full knowledge of the many inconveniences that accompany playing a left-handed guitar, I chose to do so.
Natural arm position for most people is to have the dominant arm closer to the body, and the other arm extended somewhat. You see this is many things -- a boxing stance, holding a rifle, holding a guitar, holding a violin. If you're right-handed, try doing these things in a left-handed way, with the left arm closest to your body and your right arm reaching out. I'll bet dollars to doughnuts that you find it feels strange and disconcerting.
Ned, you may know a lot about violins, but it is apparent you don't know what it's like to be left-handed. I find your comment about wanting to play a left-handed instrument being a psychological matter bothersome, and actually a bit insulting. If the only violins available to you were left-handed, and everyone told you that you had to play them in a left-handed position, would your desire to play a right-handed violin in a right-handed position be psychological? I don't think so. There are sound physiological and neurological reasons for wanting to do what feels natural.
The fact that some lefties play fine right-handed illustrates their unavoidable practice in doing some things right-handed and/or a lesser sense of their left-handedness. It does not mean that all lefties can do likewise.