The reason for a bit of exposed lead at the tip of many soft points is that it collapses on impact and starts the process of mushrooming a bit earlier than if the jacket material ran all the way to the end, and there was no exposed lead. Polymer tip bullets function in the same way, on impact, they burst open the gilding metal jacket, helping it to peel away and expose the lead.
No matter how many times you see it in the movies or read about it in fiction books, smoothing the tiny imperfections off of a bullet is not going to make factory loaded ammunition more accurate. There are hundreds of places that inaccuracy creeps in, in the ammo, in the rifle, in the environment, and so forth.
A bullet is gyroscopically stable. if it is concentric, uniform, and smooth, it is predestined to fly accurately. It would take a pretty big damaged area on a bullet to make it fly off it's axis. A miligram of misplaced metal won't do it, but as was shown in that box of truth page, a badly damaged area that screws up the streamlining and also messes up the concentricity will cause the things to spin out of control.
It would have been interesting to see what those groups looked at out at 300 yards.
Your remington core lokt are an iconic round. a solid hit with an adequate caliber, barring any unusual events, is going to drop whatever you hit. Period. and as far as accuracy, you may be able to find better factory loads for YOUR rifle, but I believe that core lokt will probably turn in accuracy equal to any other brand in at least 90% of production rifles.
My .243 would run 1" groups with factory 100 grain psp, and I never managed to better that with other brands or handloads.