Believe it or not, you were wrong. IllinoisCoyoteHunter is actually correct, from quite a number of reports I've seen and from my own recent experiments with ultrasonic cleaned vs. polished cases. It won't matter one way or the other to handgun accuracy, but rifle shooters, especially long-range rifle shooters, have found muzzle velocity variation is higher using polished cases. The current theory is that polishing allows neck brass to flow out over its contact area with the bullet jacket to get a higher friction hold on it. This is the akin to plastic wrap sticking best to smooth glass or polished surfaces better than it does to a matte surface. The problem is that the consistency of that added grip depends on uniform, contamination-free surfaces. Scratches in the neck or on the bullet, irregular dust presence, neck lube, or fingerprints on bullets, all can affect it, so uniformity of the resulting greater hold on the bullet tends to be poor.
If you already have polished rifle brass, running a neck cleaning brush inside will roughen it. Using moly or HBn or other bullet coating will prevent the polished neck and bullet surface from making intimate contact. What I don't know is whether the wax-like coating in Nu-Finish, specifically, will also serve that purpose, so I invite you all to do this experiment to see if your chambering is adversely affected:
Clean at least 17 cases just by wiping the exterior off with a rag dampened with odorless mineral spirits. Leave the inside alone. If you think there is grit inside, a denatured alcohol flush should carry it out without doing serious cleaning and should dry quickly. Clean another 17 cases with new corncob (walnut has oil in it, so it may not work for this experiment). Finally, add Nu-Finish to the corncob, run the tumbler with the lid open for 30 minutes to dry it¹. Finally, run the last 17 cases in the tumbler with the polish. Load all the cases identically and keep them separate as groups A, B, and C. Go to the range with your chronograph and get 15 good readings from each group (two of the 17 rounds are spares, in case you get a bad reading or two) to see which set produces the lowest standard deviation. Make up 4 more rounds to have an even 50. Finally, make up how ever many fouling rounds your gun needs to settle. 3 is common, but some bores need more.
Because of changing light, temperature, and bore conditions, I would fire the foulers, then fire the three groups round robin style to spread out the effects of any changing conditions you may have (bore fouling, gun temperature, incident light levels on the chronograph sky screens, etc). That is, fire one from Group A, then one from Group B, then one from Group C, recording the velocities from each group member in three columns, A,B and C on paper. Repeat until you have 15 good readings under each column. You'll then have to calculate the standard deviations of the velocities you recorded for A, B, and C in order to compare them. Putting the three columns in Excel and using the =STDEV(range) function is the easiest way.
If you don't have Excel, you can figure SD out manually with a calculator. It needs at least the square root function on it for this not to be a pain. What you do is find the average velocity for each group of 15. Then you subtract that average from each individual velocity to give you the differences. Some will be negative numbers and some will be positive numbers. Square each of them (which also makes them all positive, so you're not having to mess with any negative number arithmetic). Add up the resulting squares. Divide that sum by 14 (n-1, where n is the number of samples; 15-1 in this case), then take the square root of the result. That is standard deviation the way your chronograph calculates it. Technically it's called a sample standard deviation and serves as an estimate of the standard deviation you will have for all future identical loads fired under identical conditions. Finally you look to see which set has the lowest SD, and decide whether it's a significant difference to you or not.
This gets argued about periodically. If you expose brass to ammonia, but load and shoot the loaded ammo promptly, you may never notice the effect. If you also anneal necks periodically, that helps prevent season cracking in ammonia's presence. If you leave the brass loaded for long periods and don't anneal, then even the small amount of ammonia gas that Jcwit allows into the air can do damage just by being present in the same room with the brass. Before annealing was worked out, soldiers used to cause season cracking of ammunition in the corners of ammunition stockpile bunkers just by urinating in those corners. The ammonia from the urine breaking down was all it took. Not a lot.
The Wikipedia entry on season cracking
appears to me to be accurate, and is worth reading.
¹This should be done outdoors to avoid putting primer residue dust into the air. Unless you use non-toxic or green primers exclusively, that dust has acid and water soluble lead compounds in it that are toxic. Cleaners and case separators are the single biggest source of lead contamination in the reloading environment. Much bigger even than bullet casting produces.