We have proven this with deforming bullets that shed the nose. Rotational velocity is a significant contributor to length of penetration and straightness of penetration. Take it a step further to a bullet that is marginally stable for ballistic flight. A marginally stable bullet will fly very accurately consistently enough to compete in bench rest. This marginally stable bullet will likely have issues when impacting an animal. This where we see bullets do not expand at all. Plenty of impact vel for full expansion, so to say that stability plays no role in terminal performance is simply wrong. Or to say that it only matters for a non expanding spitzer is also wrong. No offence intended.
Another scenario that proves this it testing dangerous game solids. A shorter lighter solid that is designed not to lose any weight or expand will out penetrate a longer heavier one impacted at the same vel. Reason is that the longer shank will upset sooner and begin to tumble causing it to lose velocity sooner and penetrate less as well as going off track and changing direction. Give the longer heavier solid a higher rate of twist and it will improve the depth of penetration. The only time I would say that higher stability does not aid in straight line penetration is with a bullet has poor integrity and comes apart on impact. This really doesn't count, because bullets like this are bound for failure on tough animals or large animals requiring deep penetration. They are simply unpredictable.
While we are at it, let's blow up the theory that higher sectional density bullets will always have better penetration. I mentioned earlier that the amount of time that a bullet spends deforming and shedding weight will directly effect it's ability to penetrate. The longer this takes the more of the rotational vel and forward momentum is robbed. Let's take our 30 cal 124g Hammer Hunter with a sectional density of .187 will out penetrate other bullets of ours with much higher sectional density. Proven in media and lots of animals, big animals like water buffalo.
@fordy was the first guy to take this little pill out and shoot animals way too big for it's weight. It outperforms .375 caliber bullets in it's penetration and stopping power. At this point I only have theories on how this can happen. According to conventional wisdom it can't, but it does. Not just once, but hundreds of times. I believe it comes down to a perfect balance of shed weight, length of retained shank, and form of retained shank that creates a pressure wave in front of the bullet as it passes through the soft tissue creating a scenario where very little material is actually touching the bullet. Along with that an incredibly high stability factor. Along the same lines, we have our 137g 30 cal Hammer Hunter. Designed proportionally the same as the 124g Hammer Hunter 30 cal. It was under performing to what we anticipated. Still outperforming conventional bullet, but not what we expected. We changed the hollow point depth by 2mm and gained 18" of penetration. Now it is running with the 124g Hammer Hunter, maybe slightly better. It has not had the chance yet to test on very many bovines and such. We will see after a proper number of animals are taken with it. One more. I am pretty sure that no one here would bet that a 248g .375 cal Hammer Hunter fired from a 10" twist rum would out penetrate a 281g Hammer Hunter fired from the same rifle. I lost that bet. Both bullets loose proportionally the same amount of weight on impact. As of right now the heavier higher sectional density bullet is overlooked by the Ausies when headed out to cull water buffalo. Sectional density of the two bullets is .252 and .285. Now, that same 375 rum has a new barrel with a 7" twist. I think this will make the 281g outperform the 248g. I'm not sure though. We will soon see. I used the 281g Hammer Hunter in Africa last April and flat decked everything I shot, including a giraffe. Shoulder shot he only made it 52y. That is like three jumps for a giraffe.
So, much of the information out there about bullet performance based on sectional density and energy was written by magazine writers back in the 50's and 60's and passed on as fact, simply does not stand up to scrutiny. Repeating it and stating it as fact without your own testing to back it up doesn't hold water. I don't claim to be an expert, or the smartest guy in the room, but I have set out to figure it out, in the process of producing the best bullet possible. We assumed a lot of stuff when we started making bullets, and when it didn't work, like we assumed, we set out to figure it out so we could correct it. Terminal performance in a hunting bullet is everything. Everything else is secondary.