What wood are those arrows made of? You seem to be describing plastic nocks, so I'm wondering how a nock could have broken by putting in on the string--unless the nock groove was a whole lot smaller than the string diameter.
Just for the record, I have spine tested hundreds of shafts and have NOT found that a particular orientation of the grain is consistently stiffer than another. There is an unfortunate willingness among humans to take a few examples of something and then conclude that they represent an undeniable principle.
It is undeniable that shafts with the least runout make the best arrows.
Just for thought, what part of the force of paradox would make an arrow break up, or down?
Once when my son was about 12, we were shooting at a tossed milk jug that was stuffed with rags. After a hit, he picked up the arrow with the jug impaled on the end. Before I noticed, he had nocked and drawn the arrow with the jug on it. I hollered "No!" just as he loosed. Of coarse the arrow snapped like a tooth pick. Guess which way the pieces flew--away from the bow. The only direction there is ever any side force on a shaft.
I have seen the pictures of broken shafts (usually "unbreakable" carbon) sticking in somebody's hand. I still have to wonder how in the world they did that. (Part of me is extremely skeptical.)
I have never had an arrow break in the act of shooting, but I check my arrows when pulling them from the target or digging them out of the dirt or whatever else they hit. If a splinter has lifted anywhere on the shaft, I don't shoot the shaft again without repairing it, or if unrepairable, I break it to avoid a dangerous mistake.
Jim Davis aka Reparrow man