To me, both interpretations could be correct. It comes down to how you view the horns; on or off the cow.
Tim is correct in terms of on the cow. Horns come off the head and head downward before they start twisting upwards.
If I wanted to make a right-hand preference horn for someone (a horn whose shape would conform to the right side of the torso and have the tip pointing downward and in instead of upward and out), I'd use the horn from the LEFT side of the cow in the 1st picture.
The next pictures show a pretty good comparison between the "twists" on a horns from the right and left side of the cow.
I have never had the opportunity to select horns while they are still on the cow. I'm usually digging through a stinking pile of horns on a hot September afternoon at Friendship, looking for horns whose twists and shapes conform to the right side of the torso best. What I am looking for is best illustrated by the horn Tim calls LEFT in his picture. To me that is a right-side carry horn with the one he calls RIGHT being a left-side carry horn. I'm usually finding horns whose twists lend themselves best to left-side carry as most of the best right-side carry twists were picked out before the pile ever hit the ground.
I agree that with thoughtful cutting, shaping, and staple placement, you can force a horn to lay correctly on whichever side of the torso you prefer. I find that it is easier to do that with horns that are straighter overall to begin with. There never seems to be a shortage on the straight horns!
