A little more anecdotal tuner info:
Some time ago, Jackie gave me a pre snubber tuner. About that time Sims Vibration Lab. gave me a couple of prototype Deresonators that had larger IDs, that were designed to be used on larger diameter barrels. A friend and I fitted the tuner to a well worn barrel that I had had on my rifle since it (the barrel) was new. We turned steps on the barrel to remove the same amount of weight as the tuner plus the rubber piece weighed, approximately 5.25 oz. I did some testing which led me to believe that the barrel shot best with the rubber thing just behind the tuner threads, which are 2" long. I then shot a weekend long match, with the weirdest looking barrel, steps, deresonator and tuner. It seemed to me that the tune was broader, and that the barrel shot more true to the flags. The throat was so rough that a very small piece of steel came out on a patch after brushing. It shot better than it had before. It won its last match at 200 with a .291 at Visalia, against the usual field. This was not my usual performance.
Some time back, I persuaded Don Jackson to share his tuner experience on this board. Very briefly, he fitted simple tuners to a half dozen barrels that had been put aside after initial testing due to their not being competitively accurate. by fitting tuners, he improved the performance of 5 of the 6 by an average of .050, I believe.
Obviously no tuner can read a wind flag, but I believe that as part of a well (or accidentially well) executed system, they can improve raw accuracy.